Skvortsova, Minister of Health of Russia, said: "In Russia, mortality increases. And not due to the fact that the population is old. Increased mortality in young people - aged 30 to 45 years. The horror is that when opening the dead patients in 70% of cases, blood alcohol is detected. For the first time in recent years, the number of suicides, alcohol poisoning, not set in the lifetime of diagnoses of pneumonia in asocial groups of the population. This is a big problem"
And it can be stated that mortality in Russia has recently growing due to the increase in mortality of this age group, and not by increasing the number of old people, as Skvortsova has tried to explain. The aging of the population is one of the main reasons for increasing mortality, so in the near future mortality will only increase, spoke less than two months ago at the Selector Meeting at Medvedev Skvortsov. "An increase in mortality in adults is partly due to an increase in the life expectancy and the changed age structure of the population, the Minister told. - According to Rosstat, the contribution of the feasibility is 1.7 percentage points, therefore, with the mortality rate of 2014, according to the structure of the 2013 population, it would be lower by 27.5 thousand people. "
Experts do not agree with this. " Russia is a country with an average ratio between young and elderly, D.E.N. believes Rzhanitsyna - there are countries where the share of older people is much higher, but the mortality there is lower, and the age of waiting times is one and a half more than here. Yes, and in Russia, the life expectancy rate began not yesterday, but last year the situation was not so crying. So this version is not confirmed by our national experience, neither more experience in Europe and Japan. The aging of the population, of course, is a very convenient explanation. But the number of old men has nothing to do with it. Russia is a working age champion. And we must deal with those factors for which you can and should be influenced and which are more or less kept last year».
And Skvortsova twisted: "We can operate everything better and better, improve the work of ambulance, but nothing will change until the doctor does not take place the place of the so-called degrees - as in Soviet times. We will have to return to this. "To this phrase we will return the blog later.
So, the official data of Rosstat speaks of taller developing trends. Natural wake of Russians per year has been halved - from 0.4 to 0.8 per 1 thousand population. The birth rate began to decrease in the country: - 0.8% relative to the first half of 2014. But the main contribution to uncertain statistics has made mortality that has grown by 2.8% over the year (almost 27 thousand deaths).
The biggest increase in mortality in the first half of 2015 compared to the same period 2014 was recorded in three federal districts: Crimean (4.6%), Ural (4.4%) and northwestern (4.1%). Among the regions with the worst indicators: YNAO (mortality growth - by 12%), Republic of Karelia (by 9.3%), Sakhalin region (by 8.3%), Kostroma region (by 6.4%), Saratov region (on 5.9%), Lipetsk region (5.5%).
Negative dynamics demonstrate both capitals. IN Moscow The increase in mortality amounted to 4.9%, in St. Petersburg - 4.7%.A C.it is an anger of all spoils the statistics of Sevastopol, wheremortality from all causes has grownover the past year by 14.3%.In addition, the city has increased the number of suicides (by 10.9%) and deadly accidents (16.2%).
At the same time, in 10 Russian regions, on the results of the first half of the year, a decrease in mortality was recorded by more than 1%: in the Nenets Autonomous District (4%), Tyva (3.3%), in the Moscow region (by 2.8%), Ryazan Areas (2%), Dagestan (1.9%), Karachay-Cherkess Republic (1.2%), in Magadana and Amur regions, Ingushetia and Chukotka (1.1%). In 8 regions, this figure was less than 1%.
In some regions there is a catastrophic situation in the level of infant mortality, Despite the overall positive dynamics of decreasing mortality of babies in the country - by 13.1% per 1,000 children born. So, according to the service of the State Stast, in the Pskov region, the death rate of children under the age of 1 year increased by 86%, in second place for this indicator Kaluga region (44.8%), followed by Karachay-Cherkessia (38.5%), Republic Mari El (38%), Smolensk region (38%), Oryol region (36.6%), Murmansk region (35.2%), Kabardino-Balkaria (30%), Yaroslavl region (25.9%).Statistical figures are a fact from our reality.
To analyze the standard of living in a particular country, you need to pay attention to several factors, one of which is the life expectancy of a person. What is life expectancy in Russia in 2018-2019? Despite the fact that in the last 10 years there has been a positive dynamics, it is impossible to talk about a large SPJ in the Russian Federation.
In order to get such an indicator, you need to collect these citizens of deceased citizens. After that, their total quantity must be divided into full-length years. Thus, the indicator is averaged.
It is worth noting that such calculations for men and for women are conducted equally, but indicators, at the same time, can be varied.
Those intermediate values \u200b\u200bobtained by arithmetic operations are the base for other calculations. It turns out that the calculation of such an indicator occurs stepwise.
In Russia, such a technique is used for more than 10 years. It covers all age groups whose age is in the range from 0 to 110 years.
What is the average life expectancy in the Russian Federation?
The average life expectancy in Russia was different in Russia.
Interesting Facts:
- At the turn of the 19th and 20th century, it was 32 years. Although the same
the time period, in Europe the situation was not much better. The whole thing in wars and epidemics. People did not survive up to 40 years due to the abdominal typhoid, Spaniards and other diseases.
- Record SPZH in Russia was recorded in 2015. The indicator reached 71 (averaged indicator). This exceeded the vital duration of the population of the Soviet Union. The life expectancy of women in 2015 was 76.7 years old, and men - 65.6.
- Further dynamics could be traced in a year. By 2016, the life expectancy of a person in the Russian Federation was increased to 6 months, and in 2017 he went to the decline - only 66.5.
Dynamics of life expectancy in the Russian Federation from the 20th century
At the beginning of the 20th century, Russia has become a participant in World War and Revolution. Many people died, but even despite this, every year the life expectancy of Russians increased.
Thanks to the development of medicine, mortality of citizens decreased significantly. To analyze the dynamics of the life expectancy of Russians, you can use the table.
| Of the year | Men | Women | |
| 1926-1927 | 40 | 45 | |
| 1940 | 40,4 | 46,7 | |
| 1950-1960 | 63,7 | 72,3 | |
| 1965-1995 | 64 | 75 | |
The latest indicators have become similar European at that time. Thus, the table given above suggests that since the 1950s, the SPZh of the Russian man has increased almost 2.5 times. Although the life expectancy of men in Russia has always been lower.
This led to the fact that the conditions for the leisure of the population improved. Also positive changes have come in the field of work. Improved working conditions, production.
The economic crisis of the 1990s was strongly reflected in the fertility factor. Experts say that in addition to the crisis, such a situation can be explained by reforms of restructuring. During this period, child mortality has increased significantly. The cause of this was the collapse of the health system.
The growth of the population could be fixed after 1997. Experts believe that this has become possible due to the addictive of the population to new living conditions. Interesting fact: during this period, the SPZH men compared to the SPZH women decreased by 13 years. Only by 2006 in the Russian Federation began to appear male pensioners.
After 2015, the demographic situation has changed: the standard of living has increased significantly, the mortality rate has decreased, the health system has improved, the birth rate has increased.
Schedule of the demographic situation in Russia
In 2018, SPZH in the Russian Federation became 66.5.
SPG in cities and villages
In small settlements of Russia, the level of medical care remains low. Moreover, in some of them, medical care is not at all. This leads to a high mortality rate in some villages and villages.
But thanks to the so-called "successful regions of the country", the SPZH in the Russian Federation increases. Demographic problems exist in those areas in which funding is insufficient. As practice shows, the budget in such regions is not balanced.
Middle age of the population in the Russian Federation and other countries of the world: a comparative analysis
In 2018, the Russian Federation took 110th place in the Rating on the SPG in the countries of the world. Experts believe that SPZh in the Russian Federation remains low for several decades. In such developed countries, such as, for example, Japan, France or Singapore, this figure is approximately 80.
The conclusion is obvious: Russia lags behind this indicator from developed countries, while in the 1960s, the average agents of European countries and Russia were approximately equal.
In which countries this indicator is higher?
In which countries this indicator is almost the same as in the Russian Federation?
| Country | Average age |
| Hungary | 73 |
| Romania | 72 |
| Estonia | 72,5 |
| Latvia | 71 |
As for the CIS countries, the indicator of the SPG in them is different.
Why in the Russian Federation a low indicator of SPG citizens?
First of all, this indicator depends on the mortality rate. And in the Russian Federation, this coefficient has remained rather high for many years. Such a phenomenon is atypically for Western European countries.
The following factors have a huge impact on this situation:
- The level of economic development of the country. For this parameter, Russia occupies 43rd place in the world.
- The level of education. For this parameter, Russia occupies 40th place in the world.
- The level of income of the population. For this parameter, Russia takes the 55th place in the world.
- Index social. development. For this parameter, Russia ranks 65th in the world.
Most experts believe that such an indicator as the average life expectancy, primarily depends on the level of medical care in the country. The health of citizens depends not only on the economy, but also from the health system.
In some regions of the Russian Federation, medicine is not simply low on its development, it may be absent at all. This is a big problem for Russia, relevant in our time.
Russians of old age often remember Soviet times, nostalging. They remember the price level, accessibility of housing and collective consciousness. This period, many noted as stable. With regard to the modern period of the country's development, it cannot be called stable due to political and economic reasons.
To properly ask a question, you need to know most of the answer. (Shekley)
Distribution of life expectancy and mortality table
Introduction
Insurance can increase the expected utility for a person who has risks random losses. The basis of simple models for insurance contracts concluded for one time period are Bernoullievsky random variables that reflect the offensive or unaccompanies of the insured event.
The occurrence of the insured event in some examples leads to another random process determining the magnitude of the loss. There are models of insurance systems designed to work with random losses in which the accident is associated with how long a certain person will live.
The main structural element of such models is a random value called the duration of the upcoming life (time of survival) and denoted by T (x).
So, we present a number of ideas that will allow you to describe and use the distribution of both this random variance and the corresponding age at the time of death.
We will show how the distribution of the random variable "age at the time of death" can be represented by means of a mortality table. These tables are useful in many areas of knowledge. Therefore, in each of these diverse areas where mortality tables use, its terminology and notation has been developed.
For example, engineers use mortality tables to study the reliability of complex mechanical and electronic systems.
In biostatistics, the mortality table is used to compare the effectiveness of various methods of treating serious diseases.
Demographers use mortality tables as a means of population design. We will use mortality tables to build insurance systems designed to promote people who are in the face of uncertainty associated with the moment of their death.
The mortality table is an indispensable component of many models of actuarial science. Some researchers consider the date of birth of actuarial science 1693. This year, Edmund Gales (E. Halley) has published the work of "An Estimate of the Degrees of the Mortality of Mankind, Drawn From Various of Births and Funerals at the City of Breslau" ("Assessment of the degree of mortality of mankind derived from various tables of birth and Breaks in the city of Breslavl ").
Mortality Tables, named by Breslavl, which are contained in the Gallet Article, are still of interest due to an amazingly modern system of designations and concepts.
Probability relating to age at the time of death
We describe the uncertainty associated with age at the time of death, in probabilistic terms.
Function of survival
Consider a newborn. Age at the time of death X for this newborn is a random magnitude of a continuous type. Denote by the function of the distribution of this random variable,
and put
We will always assume that, from where it follows that S (0) \u003d 1.
The function s (x) is called function to live. For any positive x the value of S (x) is the likelihood that the newborn will reach the age of x. Distribution S.V. X can be determined either by specifying the distribution function or the function s (x).
In the actuarial science and in demographics, the recovery function was traditionally used as an initial point for further research.
In probability theory and in statistics, the distribution function plays such a role. However, from the properties of the distribution function, we can derive the corresponding properties of the recovery function.
Relying on probabilistic laws, we can formulate probabilistic statements about age at the time of death in terms or the recovery function, or distribution functions.
For example, the likelihood that the newborn will die in between x and z (x The conditional probability that the newborn will die at the age of between x and z, provided that he lives to the age of x, equal The symbol (x) is used to designate the face of the age x. The duration of the upcoming life of this person (x), x - x is denoted by T (x). Actuarial characters differ from the designations adopted in the theory of probability, and the reader may not be familiar with them. For example, the function of one variable, which is written as Q (X) in the likely notation, will be recorded in the form of QX. Similarly, the function of many variables is written in actuarial notation using a combination of upper and lower indices and other characters. For the formulation of probable statements about T (x) we will use the notation The symbol can be interpreted as the likelihood that (x) will die over the next T years. In other words, the distribution function S.V. T (x). On the other hand, it may be interpreted as the likelihood that (x) will reach the age of x + t. In other words, it is a function of surviving for (x). In a particular case of persons aged 0 we have T (0) \u003d x and If T \u003d 1, by agreement, we can omit the first index in the notation introduced by formulas (2.4) and (2.5), receiving qx \u003d p [(x) will die for one year], px \u003d p [(x) lives to age X + 1 years]. There is a special symbol for a more general event consisting in the fact that (X) will live t years and die over the next U years, i.e. that (x) die at the age between X + T and X + T + U, namely As before, if u \u003d 1, then the corresponding lower index is lowered in the designation, and we get a symbol. Now we have two expressions for the likelihood that (x) die at the age of x and x + u. Formula (2.7) at T \u003d 0 gives the first of these expressions, and formula (2.3) with z \u003d x + u is the second expression. Will these two probabilities be different? Formula (2.3) can be interpreted as a conditional likelihood that the newborn will die in between x and z \u003d x + u, provided that it lives to the age of x. The only information about the newborn, by now the age of the age, is that he lived before this age. Therefore, the probability statement under consideration is based on the conditional distribution, subject to survival for newborns. On the other hand, formula (2.7) at T \u003d 0 determines the likelihood that the person observed at the age of the age will die in the age of x and x + u. Data on the face at the age of C may contain not only information that it has survived to this age. This may be information that the person under consideration has passed a medical examination before the conclusion of the insurance contract, or that this person has just started a course of treatment from a serious illness. Mortality Tables in the case when data on the face at the age of X contains not only information that the newborn has survived to age X, discussed in, where additional designations are introduced for these tables. We will continue to develop the theory, assuming that formulas (2.3) and (2.7) do not contain semantic differences, i.e. we will consider it to consider that information about the face that lived to the age of x, gives the same conditional distribution of the duration of the upcoming life as the information about the newborn to the age of the ages, namely With this approach of formula (2.7) and many of its special cases can be expressed in the form With the duration of the upcoming life, a discrete random variable is connected, which determines the number of fully years of those who lived by the face (x) to death. It is called a step-by-step duration of the upcoming life of the face (x) and is denoted by to (x). Since S.V. K (x) is the largest integer that does not exceed T (x), its probability function is set by the expression k \u003d 0,1,2, ... (2.11) The change of inequalities in places here is possible, since under our assumptions that the distribution of T (x) continuously, p [t (x) \u003d k] \u003d p \u003d 0. Formula (2.11) is a special case of formula (2.7), where U \u003d 1 and K is a non-negative integer. From the ratio (2.11) it follows that the distribution function S.V. K (x) is a stepped function and and K is a whole part of the number. Often, it is clear from the context that T (x) is the duration of the upcoming face of the face (x). In this case, we will write T instead of T (x). Similarly, we will write to instead of K (x). Formula (2.3) expresses in terms of the distribution function and in terms of the recovery function, the conditional likelihood that the person (0) will die at the age of x and z under the condition, provided that it lives to the age of x. If the difference Z-x is constant and is equal to, say, then considered as a function from x, this conditional probability describes the distribution of the probability of death in the near future (between the time of time 0 and c) for the person who has reached the age of x. Analogue of this feature, considering death at a certain point, can be obtained using the density of the probability of death upon reaching the age X, i.e. formula (2.3) s, In this expression We get From the properties of functions In actuarial science and in demographics is the intensity of mortality. In the theory of reliability, which is engaged in the study of probabilities of trouble-free operation of mechanisms and systems, this value is called the intensity of failures. Like the recovery function, the intensity of mortality can be used to determine the distribution of S.V.Kh. To do this, replace in formula (2.13) x on y and after some transformations we get Integrating this expression from x to x + n, we get Potentiation getting Sometimes it is convenient to rewrite formula (2.14) by making the substitution S \u003d Uh: In particular, we will change the designation so that they are appropriate to be used in formula (2.6), putting the age of already living faces equal to 0 and denoting the age of survival through x. Then we get Moreover, and Let be It means it is the probability that the person (x) will die at the age between T and T + DT, and where as the upper integration limit is recorded "plus infinity" (this is an abbreviated recording of integration throughout the region of changing the density function lying on a positive semi-axis). From formula (2.19) it follows that This equivalent form is useful in some reasoning actuarial mathematics. Insofar as In the lower half of the table 2.1. Some ratios are collected between the standard features of probability theory and features characteristic of applications related to age at the time of death. You can bring a lot of examples when the ratios associated with age at the time of death can be reformulated in more common probabilistic terms. The following example is illustrated. Example 2.1. If indicates the addition of events and in some selective space and if, the following ratio is a probabilistic identity I rewrite this identity in actuarial designations for events Decision. The probability is rewritten in the form turns into So we get Table 2.1. Some functions for S.V. X, age at the time of death The published mortality table usually contains the values \u200b\u200bof basic functions located in the ages of individuals and, possibly, additional functions obtained from them. Before submitting such a table, consider the interpretation of such functions, which is directly related to the probabilistic functions discussed in Section 2. In formula (2.9), we expressed a conditional likelihood that the person (x) will die during T years, as follows: and in particular, We now consider a group of L0 newborns, putting, for example, L0 \u003d 100,000. For each newborn, the random value "Age at the time of death" has a distribution specified by the recovery function S (x). We will be denoted by l (x) the number of persons in the group who lived to age x. We assign all persons in the group number J \u003d 1,2,3, ..., L0 and note that where is the label indicator of the face with the number J, i.e. Since E \u003d s (x), then We denote E [λ (x)] through lx, which means that LX is a mathematical expectation of the number of people who lived to age from L0 newborns, and we have Further, under the assumption that the IJ indicators are mutually independent, λ (x) has a binomial distribution with parameters N \u003d L0 and P \u003d S (x). Note, however, that in equality (3.1) does not require an independence assumptions. Similarly, we denote by the PDX the number of dead aged between X and X + P from the initial aggregate consisting of L0 persons. We denote E [PDX] through PDX. Since for a newborn, the likelihood of death at the age of x and x + n is equal to S (x) - S (x + n), using reasoning, which was reduced above relative to LX, we obtain If n \u003d 1, we omit the left lower index in the PDX and PDX expressions. From formula (3.1) it can be seen that Insofar as the lateral LXμ (x) in (3.4) can be interpreted as the expected density of deaths in the age range (x, x + dx). Note, further that For the convenience of references, we will call a group of L0 newborns, each of which has a function of surviving S (x), a set of random survival. In the table below. 3.1, which is called "Population Mortality Table: USA, 1979-1981", Functions TQX, LX, TDX are presented for L0 \u003d 100000. With the exception of the first year of life, T value in TQX and TDX tabulizable functions is 1. Other functions contained in this table are considered in Section. 3.5. This table was not created on the basis of observations of 100,000 newborn, up to death of the last of them. It was based on the estimates of the probabilities of death, subject to reconciliation to various ages received from the US population data during the years close to the 1980s, the year of the census. Using the concept of a set of random survival, we must make the assumption that the probabilities obtained on the basis of this table will correspond to the life expectancy of those who belong to this totality of survival. It is useful to make a number of comments on the table below. Comments. It is expected that approximately 1% of newborns included in the totality of survival will die in the first year of life. It should be expected that approximately 77% of the newborn group will live to the age of 65. The maximum number of deaths in the group is expected between 83 and 84 years. There are few cases when death occurs in the age of over 110 years. Therefore, it is often assumed that there is such age w, that S (x)\u003e 0 for x< w и s (x) = 0 для x>\u003d w. If the existence of such age W is supposed, it is called the ultimate age. For the table of the table, the ultimate age is not defined. Obviously, there is a positive probability to live to 110 years, but the table does not contain instructions on the age w. Local minima for the expected number of deaths are located in the region of 11 and 27 years, and a local maximum in the area of \u200b\u200b24 years. Although the LX values \u200b\u200bwere rounded to integer numbers, in accordance with formula (3.3.1), this is not necessary. Such a presentation of information as Table. 3.1, is the standard method for describing the distribution of age at the time of death. Another way is to represent the recovery function in analytical form, such as S (x) \u003d E-CX, C\u003e 0, X\u003e \u003d 0. However, most mortality research among people for the needs of insurance uses the representation S (X) - L0x / LX, which is illustrated Table.3.1. Since the value of 100000s (x) is represented only for integer values \u200b\u200bX, when calculating S (x), it is necessary to resort to interpolation for non-target arguments. This question is discussed in section. 3.6. Example 3.1. Using table. 3.1, we calculate the likelihood that face (20) 1) live to age 100, 2) dies, not to survive up to 70 years, 3) dies in the tenth decade of his life. 1) 2) To evaluate the role of mortality tables, consider Fig. 3.1, 3.2 and 3.3. They reflect the current population mortality, and not the data given in Table. 3.1. In fig. 3.1 We must pay attention to the following: The intensity of mortality is positive, and the requirement is obviously completed. The intensity of mortality is quite high at the initial stage, and then sharply decreases to a minimum in the neighborhood of age of 10 years. In fig. 3.2 and 3.3 need to pay attention to the following: The function lxμ (x) is proportional to the density function S.V. "Age at the time of death" for the newborn. Since LXμ (X) is an expected density of deaths at the age of X, when it comes to a set of random survival, the graph of the function LXμ (X) is called the mortality curve. The LXμ (X) function has a local minimum in the surroundings of the age of 10 years. Fashion distribution of deaths, i.e., age in which the maximum mortality curve is being implemented in the region of 80 years. The LX function is proportional to the Lxμ (X) functions. It can also be interpreted as an expected number of people who lived to age from the entire source group, which consisted of L0 people. Local extremum points LXμ (x) functions correspond to the location points of the LX function, since 4. A combination of deterministic survival Let us turn to the second, incredible, interpretation of mortality tables. From the point of view of mathematics, it goes back to the concept of the disposal ratio (negative growth) and therefore is associated with applications to problems of growth rate in biology and in the economy. It is by nature deterministic and leads to the concept of a totality of deterministic survival, or cohorts. The totality of deterministic survival, as follows from the mortality table, has the following characteristics: Initially, it consists of L0 people of age 0. For members of the aggregate at any age, actual annual mortality rates (disposal) are valid, which are determined by QX values \u200b\u200bin the mortality table. The aggregate is closed. No one can enter it, except those L0 people who were in her at the very beginning. The output from this set is due to the actual annual coefficients of mortality (disposal) and only by them. From the given characteristics implies that ………………………….. (4.1) where LX denotes the number of persons who lived to the age of the cuisine. This chain of equalities generated by the number L0, called the root of the mortality table, and the set of QX values, can be rewritten as ………….. (4.2) There is an analogy between the set of deterministic survival and the model of complex interest, some provisions of which are summed up in Table. 4.1. Table 4.1. The concepts of the theory of complex interest and the corresponding concepts in the theory of sets of deterministic survival Compound interest A combination of survival A (T) \u003d Capital value at time t, time is measured in years lX \u003d group size X, age is measured in years Effective annual interest rate (increment) Actual annual mortality rate (retirement) Effective N-long interest rate, starting from time t The actual-year mortality rate, starting from the age x Percent number intensity at time t The intensity of death at the age of Table columns headers. 3.1 For TQX, LX, TDX refer to the aggregate of deterministic survival. Although the mathematical foundations for the aggregates of random and deterministic survivors are different, the functions of TQX, LX, TDX have the same mathematical properties and are analyzed equally. The concept of a totality of random survival has the advantage that allows the whole apparatus of probability theory. The combination of deterministic survival is conceptually easier and easier to use it, but it does not reflect the random oscillations of the number of people who lived to a certain age. We derive expressions for some commonly used characteristics of distributions S.V. T (x) and k (x) and we introduce a general method for calculating some of these characteristics. Mathematical expectation S.V. T (x), denoted by èx, is called the full life expectancy. Using integration in parts, we will get From existence E should ratio The full life expectancy in different ages is often used to compare public health levels of various countries. Similar integration in parts gives an equivalent expression for E: This result is useful for calculating D [T (X)] by the formula In all the above calculations, we assumed that E and E exist. You can construct the program of the survival S (x) \u003d (1 + x) -1, for which it will not be. You can define other distribution characteristics S.V. T (x). Median duration of the upcoming face of the face (x), which is denoted by m (x), can be found as a solution of the equation or relative to M (x). In particular, M (0) is a solution of the equation s \u003d 1/2. We can also find the distribution modes S.V. T (x), specifying the value T, which delivers the maximum value of the TPXμ function (X + T). Mathematical expectation S.V. K (x) is denoted by EX. This value is called a step-by-step expected lifetime. Applying and described in Appendix 5 summation in parts, we get Again from the existence of E [k (x)], the ratio Limkk-\u003e ∞ (- KPX) \u003d 0. Thus, having replaced the variable on which the summation is carried out, we have Repeating reasoning spent for a continuous model, and using the summation formula in parts, we get From the existence of E [k (x) 2], the ratio of Limkk-\u003e ∞K2 (- KPX) \u003d 0. When replacing the variable, according to which the summation is made, we get To complete the discussion of some component tab. 3.1 We must enter additional features. The L2 symbol denotes the total anticipation of the number of years live between the ages x and x + 1, which lived to ages from the source group, containing Lo newborns. We have where the integral in the right part is equal to the number of years lived those who died in the age range between X and X + 1, A LX + 1 equal to the number of years lived in the age range between X and X + 1 those who lived to the age of x + one. Integration in parts gives The LX function is also used in determining the transmission coefficient in the interval between X and X + 1, which is indicated by MX, where The above definitions for MX and LX can be distributed on the racial length intervals other than the unit: For a set of random survival of NLX is a common expected number of years that live in the age range between X and X + N who have lived to ages from the initial group containing L of newborns, and NmX is a transmission coefficient of mortality that was observed in this group on the interval ( x, x + n). The TX symbol denotes the total number of years leaving after reaching the ages with people who lived to this age from the source group containing L0 newborns. We have The latter expression can be interpreted as an integral of total time, lived between the ages of X + T and X + T + DT by a group of LX + T people who lived to this age interval. We also pay attention to that TX is the limit of NLX, when n strives for infinity. The average number of years of the upcoming life for LX people from the group who spent to age X is determined by the expression We can find an expression for the average years of years live between the ages of X and X + N by a group of LX people who lived to the age of x: This feature is a truncated (on the N-year interval) of the full life expectancy for persons (x) and is denoted by. The last function associated with the mortality table described in this section is the average number of years live between the ages of X and X + 1 by those in the group of those who lived to the age of x, which dying at some point between these ages. This function is denoted by α (x) and is determined by the relation With a probabilistic look at the mortality tables, we would get If we assume that i.e. if the moments of death are evenly distributed within the annual age interval, then we will get This is the usual approximation of the α (x) function, suitable for people of all ages, except for the very young and very old, where, as fig. 3.2, this assumption may not correspond to reality. Example 5.1. Let's show that Decision. From (5.11), (5.12) and (5.18) we get The formula can be substantiated, approaching the integral in (5.12) using the Formula of the trapezium 5.2. Recurrent formulas Example 5.1 illustrates the use of numerical analysis to find the characteristics of mortality tables. For approximate integration, the formula of the trapezium is used. To illustrate another computing method, which uses recurrence formulas, consider the calculation of full and step-by-step expected life extensions. When applying recurrent formulas, we will use one of the following two forms: reverse recurrent formula direct recurrent formula The variable X usually accepts integer non-negative values. Table 5.1. Reverse recurrent formulas for ex and To calculate the function U (x) with integer non-negative values \u200b\u200bx, we need to know the corresponding values \u200b\u200bof functions with (x) and d (x) and the initial value of the function and (x). This procedure is used in subsequent chapters and is illustrated in Table. 3.5.1, where to calculate EX and reverse recurrent formulas are used. 6. Assumptions for fractional ages Previously, we discussed a continuous random value of T, the duration of the upcoming life, and the discrete random amount of the forthcoming duration of the upcoming life. The mortality table, presented in Section 3, fully determines the distribution of probabilities S.V. K. To determine the distribution of S.V. T We must postulate some analytical form or based on the mortality table, adopting some assumption about the structure of the distribution between the whole points. Consider three widespread assumptions used in the actuarial science. They will be formulated in terms of live functions and in such a form, which allows the nature of interpolation on the interval (x, x + 1) arising from each of these assumptions. In each statement x is the whole and 0<=t<=1. Сформулируем предположения: Linear interpolation: S (x + t) \u003d (1 - t) s (x) + t s (x + 1). This leads to a uniform distribution or, more precisely, to the uniform distribution of the moments of death within each one-year age interval. In this case, the assumption TPX is a linear function. Indicative interpolation, or linear interpolation for ln (S (X + T): Ln (S (X - 1)) \u003d (1 - T) ln (s (x) + t ln (s (x + 1)). This Consistent with the assumption of the constant intensity of mortality within each one-year age interval. In this case, the assumption TPX is an indicative function. Harmonic interpolation: ln (x + t) \u003d (L - T) ln (s (x)) + t ln (S (x + L)). This is what is called the assumption of hyperbolicity (historically, the assumption of Balducchi, since in this case the TPX is a hyperbolic curve. Relying on these basic definitions, for the remaining standard probabilistic functions, it is possible to derive the formula in terms of probabilities specified in the mortality table. Such results are presented in Table. 6.1. Note that we could formulate the equivalent definitions in terms of the density function, distribution function or mortality intensity. The output of the expressions included in Table. 6.1, it is simply an exercise consisting in the substitution of the assumptions formulated above S (X + T) into the corresponding formulas sections 2 and 3. We will demonstrate this process for a uniform distribution of deaths. To determine the first expression in a column relating to a uniform distribution, start with the ratio and then we substitute the corresponding expression for S (X + T) and get For the second expression, we use the formula (2.13) and The division of the numerator and denominator in the right part on S (X) leads to the formula The third expression is a special case of the fourth at y \u003d 1 - t. Considering the fourth expression, let's start with equality then substituting the corresponding expression for s (x + t) and s (x + t + y), we get The fifth expression is the addition of the first, and the last expression in the column relating to the uniform distribution is the product of the second and fifth expressions. Table 6.1. Probabilistic functions for fractional ages If, as before, x is an integer, then the analysis can be carried out by entering the random value of S \u003d S (x), such that Where t is the duration of the upcoming life, to - a step-by-step duration of the upcoming life, a S - a random variable representing the last fraction of the year, in which death has come. Since K is a non-negative integer random value, a S - random magnitude of a continuous type, the whole mass of which is concentrated on the interval (0.1), we can explore their joint distribution, writing P [(k \u003d k) ∧ (s<=s)]=-P(k Now, using an expression for S q x + K under the assumption of the uniformity of the distribution, as shown in Table. 6.1, we get P [(k \u003d k) ∧ (s<=s)] = kPx sPx+k = k|qxs = P(K = k)P(S<=s)... (6.2) Thus, the joint distribution of St. K and S can be decomposed on the work of marginal distributions S.V. K and S. Therefore, in the assumption of the uniformity of the distribution of moments of death S.V. K and S are independent. Since the distribution P (s<=s) = s является равномерным на (0,1), св. S имеет именно такое равномерное распределение. Example 6.1. Will there be sv. K and S are independent in the assumption of constant mortality intensity? Decision. Taking advantage of the information from Table. 6.1, relating to the selence of the permanent intensity of mortality, we get P [(k \u003d k) ∧ (s<=s)] = kPx sPx+k = kPx To discuss this result, we will distinguish between two cases: If the expression for Px + is knocked, then we cannot imagine the joint distribution of SV. K and S in the form of a product of marginal distributions. From here we conclude that S.V. K and S are not independent. In the particular case, when px + k \u003d px- constant, For this particular case, we get that S.V. K and S are independent under the assumption of constant intensity of mortality. Ў Example 6.2. We show that in the assumption of uniformity of death distribution Decision. (a) (b) d [t] \u003d D. From independence of sv. K and 5, in the assumption of the uniformity of the distribution of deaths, we obtain D [T] \u003d D [k] + d [s]. Next, since S.V. S is evenly distributed on (0.1), D [T] \u003d D [k] + 1/2. Ў 7. Some analytical mortality laws There are three main arguments in favor of making an analytical expression for the mortality rate or for the recovery function. The first is philosophical. Many phenomena studied in physics can be effectively explained by simple formulas. Therefore, based on biological considerations, some authors suggested that survival in the human community is managed by the same simple laws. The second argument is practical. The function with several parameters is easier perceived than the mortality table with, possibly 100 parameters or probabilities of death. In addition, some of the analytical expressions have simple properties that are convenient when withdrawing probabilistic statements relating to more than one person. The third argument for simple analytical functions of survivors is the ease of evaluating the parameters of this function based on mortality data. In recent years, enthusiasm for ordinary analytical functions has significantly decreased significantly. Many believe that faith in universal laws of mortality is naive. With all the increasing speed of computers, the benefits of some analytical expressions during computations relating to more than one person are no longer played by a significant role. However, as a result of some recent studies, biological arguments were revived in support of the analytical laws of mortality. In tab. 7.1 There are several families of simple analytical functions of mortality and survivors corresponding to various well-known laws. For the convenience of references indicate the names of the laws underlying them, and the date of publication. Table 7.1. Mortality and survival functions for various distributions Source distribution Restrictions De Moavr (1729) Hompers (1825) eXR [-m (CX-1)] In\u003e 0, c\u003e 1, x\u003e about Maichem (1860) eXR [-Ax-M (CX-1)] In\u003e 0, a\u003e \u003d -b, c\u003e 1, x\u003e 0 Weibull (1939) k\u003e 0, n\u003e 0, x\u003e \u003d 0 We note the following facts: Special characters are determined by formulas M \u003d b / ln (C), u \u003d k / (n + 1). The Act of the Homper is a special case of the Macema law at a \u003d 0. If C \u003d 1 in the laws of the homard and the mekem, then we come to the indicative (constant intensity of mortality) distribution. When considering the Law of the Makeem, it was believed that the constant A responds to an accident, and the expression of adventure. Expressions in column S (x) Table. 7.1 were obtained by substitution in (2.16). For example, for the Macema law where m \u003d in / in s. In section. 2 was considered as two ways to interpret the value of TPX, the likelihood that the person (x) lives to the age of x + t. The first interpretation was that this probability can be calculated based on the reconciliation functions for newborns with a single assumption that the newborn live to the age of x. This interpretation has become the basis for the designation and to derive the formulas. The second interpretation was that additional information about the face of the age X can make the initial function of surviving unsuitable for calculating probabilistic statements on the duration of the upcoming life of the face (x). For example, some person can undergo a survey and be accepted for insurance at the age of the age. The presence of this information would assume that the distribution of the duration of the upcoming life of the person (X) differs from the one that we would consider suitable for the face of the age x if they did not have this information. The second example: some person can become disabled at the age of the age. This information allows us to assume that the distribution of the duration of the upcoming life of the person (x) is excellent on the corresponding distribution for the person who has not become disabled at the age of the age. In these two examples, preference should be preferred by the special intensity of mortality, which takes into account specific information, which becomes known at the age of the age. Without this particular information about (x), the intensity of mortality after time t will be the function of only the achieved age X + T, which in the previous section was designated through μ (x + t). If additional information is known at the time of X, the intensity of mortality at the time x + is the function of this information at the time x and the value of T. We will denote it through μx (t), where the age of x, in which additional information was available, and the value of T was specified separately. Official information in an explicit form in this designation is not included, but clear from the context. In other words, a complete model for such persons is a set of recovery functions, one for each age, which has information about the adoption for insurance, disability, etc. This is a set of recovery functions can be perceived as a function of two variables. One variable is an age at the moment of selection (for example, at the time of issuing an insurance contract or the offensive of disability) [x] and the second variable - the time passed since the issuance of the contract or from the moment of selection t. Then each of the conventional functions of the mortality table, corresponding to such a function from two variables, is a two-dimensional array of [x] and t. We use square brackets here to note the variable related to age in which the selection was carried out. When the presence of selection appears from the intensity of mortality, we will lower square brackets in order not to complicate the designations. Schematic diagram in fig. 8.1 illustrates these considerations. For example, suppose there is some special information about the group of people engaged 30 years. Maybe they were accepted for insurance, and maybe became disabled. For these individuals, you can build a special mortality table. The conditional probability of death in each year from the moment of selection will be denoted by Q + i i \u003d 0,1,2, ..., and will be included in the first line in Fig. 8.1. The index fits the two-dimensional nature of this function, where age is concluded in square brackets, that is, the reconciliation function in the first line relies on the specific information that has been aged 30 years. The second line in fig. 8.1 will contain the probabilities of death for persons relative to which specific information has become known to age 31. In actuarial science, such a two-dimensional mortality table is called a breeding table of mortality The path for the aggregate of survival, which has been seen at the age of [x] Line connecting cells for those who have reached the same age, after 15 years from the date of selection Another way for the aggregate of survival after 15 years from the date of selection; These probabilities comprise a final mortality table. Fig. 8.1. Selection, final and aggregative mortality, 15-year selection period Remarks In biostatistics, the [x] index of the breeding table is not obliged to be age. For example, in studies of oncological diseases [x], it may be a classification index, which depends on the size and location of the tumor, and the time after selection will be counted from the moment of diagnosis. The final mortality rate, after a 15-year period of selection, for age [x] + 15, should be assessed using observations from all cells, the form [x - j] + 15 + j, j \u003d 0,1,2, .... therefore q [x] +15 \u003d qx + 15-standing by weighted average mortality estimates for various groups of selection. If the effect of selection is enough The effect of selection on the distribution of the duration of the upcoming life of T can be reduced as it removes from the moment of selection. Outside a certain time interval q for individuals of the same age will be essentially equal regardless of age at the moment of selection. More precisely, if there is a smallest integer R, such that | q [x] + r-q + r + j | Less than some small positive constant, for all ages of selection [x] and for all J\u003e 0, it would be economically to construct many selection and final tables, cutting a two-dimensional array after the R + 1 column. For temporary intervals, superior to r, we can use the ratio The first r years after the time of selection make up a selection period. The resulting array contains some set of mortality tables, one for each age of selection, and for one age of selection, elements of the mortality table are arranged horizontally during the selection period, and then vertically in the final period. This is shown in Fig. 8.1 arrows. In the studies of mortality conducted by the society of actuaries for individuals who were insured under the standard contract of individual life insurance, a 15-year selection period was used (see Fig. 8.1), i.e. it is considered that Outside the period of selection of the probability of death is supplied with one index achieved by age, i.e. Instead of Q + R +, QX + R is running - for example, at r \u003d 15 and instead of Q + 15 and instead of Q + 20, Q45 is written. The mortality table in which functions are given only for the ages achieved is called an aggregative table. Such, for example, is Table. 3.1. The last column in the selection and final table is a special aggregative table, which is commonly referred to as the final table, reflecting the use of selection. Table 8.1 contains the probabilities of death and the corresponding values \u200b\u200bof the functions L [x] + K from the publication "Permanent Assurances, Females, 1979-82, Tables", published by the Institute and Faculty of the UK Actuaries. It is called Table AF 80. This table has a two-year selection period, and it is easier to use it for illustrations than tables with a 15-year period, such as "Basic Tables", published by the United States Actuaries. Table 8.1. Exposure from the selection and final table AF 80 In tab. 8.1 We have three probabilities of mortality for age 32, namely q \u003d 0.000250< q+1 = 0,000352 < q32= 0,000422. The ordering of these probabilities is understandable because mortality for persons just adopted for death insurance should be lower. It can be assumed that the column (3) provides information on the final probabilities of mortality. Praphrazing the wilt phrase Ilf and Petrov from the novel "12 chairs", one can say "Statistics know everything ... about demographics." About how long people live and how the life expectancy changed as humanity develops. Statistical methods give the overall picture of the state of society and allow us to make the forecast of the expected changes. The average life expectancy (SPZh) is a forecast that is statistically calculated using probability theory, which shows how many years there will be people who born either at a certain age. The calculation is performed on the specified calendar year, the assumption is made that the mortality rate for all age groups will continue the same as at the time of the study. Despite the presence of conventions, the indicator is stable and not subject to sharp fluctuations. The law of large numbers plays his role, another tool for statistical research. In fact, the average life expectancy is the mortality rate of the population. The first calculation techniques appeared in the ancient times and were improved as mathematics, statistics and demographics develop. For example, it became separate or differently to take into account infant mortality. In developed countries, she is small and does not distort the overall picture. A different situation in poor states looks like, where the mortality rate of babies is high, but most of the most risky period of the first three years later retains strong health and disability before older years. If the life expectancy was calculated as the arithmetic average of all the dead, then a number was obtained, which is really not reflecting the mortality of the working-age population. The technique used in Russia covers age groups from 0 to 110 years. You can get acquainted with the algorithm by reference. In the Russian method, medium-sized arithmetic groups are used as an intermediate result for further calculations, where stepwise, the indicator on which can be judged by the demographic situation in the country, is gradually accepted through the formulas of probability theory. Sometimes they mistakenly believe that SPJ is the average age of the dead during the year. Indeed, the regimens are sent to Rosstat such information in the form of tables. Corpan statistics on the dead are used for calculations as one of many introductory. The final results may coincide, but this is extremely rare. In the literature and scientific use are used two terms: They are synonyms and denote the same thing. The second - Ceing with English Life Excectancy, entered Russian and became more often used as scientific cooperation with demographers of the whole world expands. Despite the complex internal situation in Russia, associated with a protracted economic crisis and external influence due to sanctions from a number of countries and organizations, 2015 was marked by a demographic record. The average life expectancy of men amounted to 65.9 women - 76.5, total - 71.4 years. Never before the Russians did not live for so long. The results of 2018 will be summed up by March 2019, but now, according to preliminary calculations, an increase in the overall indicator is expected, at a minimum, for 8 months. If the forecast is faithful, the male figure approaches 66.8, and for women - by 77.2 years. In 2017, the life expectancy was 72.7 years (height at 0.83 compared to 2016 - 71.87 years). " "The life expectancy rate also touched men and women. Men: 67,51 years (growth for 1.01 years compared with 2016), women: 77.64 years (growth in 0.58 years compared with 2016). http://www.statdata.ru/spg_reg_rf. All data are in open access on the Rosstat website (Federal State Statistics Service). In the same place, going to the appropriate section, you can make an interactive sample by year, time periods and groups. In pre-revolutionary Russia, the average life expectancy was about 30 years. The First World and Civil War only aggravated the situation, after which there was steady growth in Soviet times as social problems were solved and life was established. Even the monstrous losses in the Great Patriotic War of 1941-45 did not change the trend. By 1950, the indicator was: women - 62, men - 54 years. By 1990, the USSR reached a demographic peak, the overall figure throughout the country was 69.2 years. Then followed the collapse of the Soviet power, and the demographic crisis began in the Russian Federation. In the 90s, the sorrible term "Russian Cross" appeared, which was called the intersection of curves - growing mortality and falling fertility. The settlement of the population was 1 million people per year, it seemed, Russia dies. Russia has a huge, uneven populated area. The Federation consists of 85 regions with different levels of development, incomes of the population and the quality of social services. Accordingly, the life expectancy in them is not the same. Traditionally, they live in the Caucasus and in the capitals - Moscow and St. Petersburg, worse than the situation in Tuva and in Chukotka. The situation is clearly represented on the map of Russia. Statistical data with the presentation of information in the form of tables, graphs and presentations is tools for executive and legislative power to help in making decisions in domestic policies and economics. The life expectancy depends on the set of factors, the most significant of them are considered: Historically, Russia gave way to his neighbors life expectancy. The gap is saved and now. Main reasons: In 2010, according to the UN, the Russian life expectancy of 66.7 years was in a modest 136 place of the world ranking. From the republics of the former USSR, the situation was worse only in Tajikistan, Kazakhstan and Turkmenistan. In 2015, the indicator improved, Russia is still in the second hundred, but already in 110th place. For 5 years, raising by 26 points, in numerical terms - 70.5 years. Russia is among the countries with the BP in the range of 71.1-69.7 years. Given the positive factors as the size of the Russian economy, the volume of foreign trade, the magnitude of the gold and foreign exchange reserves, the position of the Russian Federation in the UN ranking can be called depressing, inappropriate opportunities, unless, of course, do not take into account the positive dynamics of the last five-year plan. The main reason for the backlog of Russia for life expectancy from many prosperous countries is that there is still a high level of poverty and uneven, and sometimes unfair income distribution. Millions of people do not receive the guarantees of social protection declared by the Constitution of the Russian Federation. Crime, drug addiction, alcoholism, suicidal moods lead to early and sustainable deaths. Insufficient control of the supervisory authorities for labor protection and safety on roads contributes its share of population. Disadvantages in the work of medical institutions, public catering enterprises, non-compliance with food products Gostas reduce the quality of life, which leads to a deterioration in public health in all regions. There are many problems and everything needs to be solved. The demographic situation is very sensitive to external influences and internal processes in society. In order for the positive trends of recent years of recent years and never moved, constant attention is required by the state leadership throughout the complex of problems. The forecast is at the moment optimistic. There are many factors, some can intensify others to weaken. Statistical studies of demographic processes will allow them to specify them. As is well known, there are more than 60% of all deaths on diseases of the circulatory system and oncological diseases in Russia. If any of these two indicators even slightly decreased, we would immediately see a decrease in total mortality in the country. Eduard Gavrilov http://www.rosbalt.ru/russia/2016/02/11/1488872.html The Government of the Russian Federation is confident that Russia will continue to grow in the UN ranking. By 2020, life expectancy should increase to 74 years, and the population of Russia is up to 147.5 million people. Prime Minister Dmitry Medvedev https://ria.ru/society/2012/1403490899.html We have a sharp jump in the life expectancy of men for 7 and a half years in recent years. This is one of the leading results in the world. Health Minister Veronika Skvortsova. https://ria.ru/society/20151002/1295379439.html If the government fulfills plans for a real increase in the incomes of the population and improving the quality of life, then the life expectancy will continue. The population can help the government in performing this demographic task if it will take care of his health, refusing bad habits and actively engaging in physical education and sports. The Russian public regularly puts forward a proposal to make an indicator of the average life expectancy in the regions to determine the efficiency of local authorities. The initiative did not find legislative support, but not discontinued from the agenda. After all, the mortality rate and the magnitude of the survival in all groups of the population clearly show the state of society and the social security of its citizens. The duration of the upcoming life for the face at the age of
(2.8)
(2.9) Step-by-step duration of the upcoming life
Mortality intensity
It is a function of the density of the continuous random variable "age at the time of death." Function 
In formula (2.12) can be interpreted in terms of conditional densities. For each age x, it gives a value at the point x conditional density function S.V. X, subject to harvest to age X and denotes through.
(2.13)
follows that .
(2.14)
(2.15)
(2.16)
(2.17)
(2.18)
Indicates respectively, the distribution function and the density function S.V. T (x), the duration of the upcoming life of the person (x). Note that (see the notation (2.4)). In this way,
(2.19)
(2.20)
we have 
. In this way
Mortality Tables
Communication of the functions contained in the mortality table with a survival function
(3.4)
, (3.5)
, (3.6)
(3.7) An example of mortality table
,
Other features associated with mortality tables
Characteristics
(5.1)
. In this way,
(5.3)
(5.4)
(5.6)
(5.7)
(5.9)
(5.10)
(5.11)
(5.12)
(5.13)
(5.14)
(5.15)
(5.16)
In accordance with Formulas (5.1) and (5.2).
(5.18)
(5.20)
Selection and final tables
LIC, then the evaluation will affect the data from different cells.
Methods of determining the average life expectancy
Video: Life expectancy in Russia
Russia in the historical perspective
Table: lifespan at birth in Russia
Years All population Urban population Rural population
total men women total men women total men women
1896–1897
30,54
29,43
31,69
29,77
27,62
32,24
30,63
29,66
31,66
(50 provinces of European Russia)
1926–1927
42,93
40,23
45,61
43,92
40,37
47,50
42,86
40,39
45,30
(according to the European part of the RSFSR)
1961–1962
68,75
63,78
72,38
68,69
63,86
72,48
68,62
63,40
72,33
1970–1971
68,93
63,21
73,55
68,51
63,76
73,47
68,13
61,78
73,39
1980–1981
67,61
61,53
73,09
68,09
62,39
73,18
66,02
59,30
72,47
1990
69,19
63,73
74,30
69,55
64,31
74,34
67,97
62,03
73,95
1995
64,52
58,12
71,59
64,70
58,30
71,64
63,99
57,64
71,40
2000
65,34
59,03
72,26
65,69
59,35
72,46
64,34
58,14
71,66
2001
65,23
58,92
72,17
65,57
59,23
72,37
64,25
58,07
71,57
2002
64,95
58,68
71,90
65,40
59,09
72,18
63,68
57,54
71,09
2003
64,84
58,53
71,85
65,36
59,01
72,20
63,34
57,20
70,81
2004
65,31
58,91
72,36
65,87
59,42
72,73
63,77
57,56
71,27
2005
65,37
58,92
72,47
66,10
59,58
72,99
63,45
57,22
71,06
2006
66,69
60,43
73,34
67,43
61,12
73,88
64,74
58,69
71,86
2007
67,61
61,46
74,02
68,37
62,20
74,54
65,59
59,57
72,56
2008
67,99
61,92
74,28
68,77
62,67
74,83
65,93
60,00
72,77
2009
68,78
62,87
74,79
69,57
63,65
75,34
66,67
60,86
73,27
2010
68,94
63,09
74,88
69,69
63,82
75,39
66,92
61,19
73,42
2011
69,83
64,04
75,61
70,51
64,67
76,10
67,99
62,40
74,21
2012
70,24
64,56
75,86
70,83
65,10
76,27
68,61
63,12
74,66
2013
70,76
65,13
76,30
71,33
65,64
76,70
69,18
63,75
75,13
2014*
70,93
65,29
76,47
71,44
65,75
76,83
69,49
64,07
75,43
2015
71,39
65,92
76,71
71,91
66,38
77,09
69,90
64,67
75,59
* Starting from 2014, data taking into account the Republic of Crimea and the city of Sevastopol.
The fracture occurred in the 2000s. The country has affected. By 2012, the fertility exceeded mortality. Rosstat noted the shift and in the average life expectancy of the population, which for the first time became more than 70 years.Table: Life expectancy in the regions of the Russian Federation in 2013
№№
Region of Russia Both Men Women
№№
Region of Russia Both Men Women
1
The Republic of Ingushetia 78,84
75,97
81,32
43
Kostroma region 69,86
64,31
75,29
2
moscow 76,37
72,31
80,17
44
Ivanovo region 69,84
63,90
75,42
3
The Republic of Dagestan 75,63
72,31
78,82
45
Sverdlovsk region 69,81
63,64
75,86
4
saint Petersburg 74,22
69,43
78,38
46
Altai region 69,77
64,11
75,44
5
Republic of North Ossetia-Alanya 73,94
68,46
79,06
47
Bryansk region. 69,75
63,32
76,32
6
Karachay-Circassian 73,94
69,21
78,33
48
Omsk Oblast 69,74
63,86
75,57
7
Kabardino Balkar Republic 73,71
69,03
78,08
49
Republic of Bashkortostan 69,63
63,66
75,84
8
Chechen Republic 73,20
70,23
76,01
50
Chelyabinsk region 69,52
63,48
75,46
9
Stavropol region 72,75
67,91
77,27
51
Nizhny Novgorod Region 69,42
63,06
75,75
10
Krasnodar region 72,29
67,16
77,27
52
Tula region 69,41
63,22
75,57
11
Khanty-Mansiysk Autoglass-Ugra 72,23
67,27
77,08
53
Samara Region 69,40
63,28
75,50
12
Belgorod region 72,16
66,86
77,32
54
Vologodskaya Oblast 69,35
63,21
75,63
13
Republic of Tatarstan 72,12
66,35
77,73
55
Mari El Republic 69,30
62,82
76,13
14
Republic of Adygea 71,80
66,55
76,97
56
Komi Republic 69,27
63,22
75,39
15
Penza region 71,54
65,47
77,52
57
Republic of Karelia 69,19
63,17
75,05
16
Volgograd region 71,42
66,11
76,57
58
Vladimir region 69,13
62,78
75,44
17
Rostov region 71,39
66,34
76,28
59
The Republic of Sakha (Yakutia) 69,13
63,54
75,00
18
Tyumen region 71,35
65,97
76,72
60
Krasnoyarsk region 69,06
63,35
74,77
19
Republic of Kalmykia 71,35
65,65
77,25
61
Orenburg region 68,90
63,10
74,82
20
Astrakhan Oblast 71,34
65,91
76,72
62
Smolensk region 68,90
62,93
74,97
21
Yamalo-Nenetsky Autobogo 71,23
66,53
75,88
63
Perm region 68,75
62,61
74,89
22
Tambov Region 70,93
64,87
77,15
64
The Republic of Khakassia 68,57
62,95
74,14
23
Voronezh region 70,89
64,81
77,03
65
Kurgan region 68,27
61,93
74,97
24
Chuvash Republic 70,79
64,59
77,19
66
Primorsky Krai 68,19
62,77
73,92
25
Moscow region 70,78
65,10
76,30
67
Tver region 68,13
62,28
74,03
26
Ryazan Oblast 70,74
64,77
76,61
68
Kamchatka Krai 67,98
62,59
74,07
27
Saratov region 70,67
65,01
76,19
69
Khabarovsk region 67,92
62,13
73,96
28
Lipetsk region. 70,66
64,56
76,77
70
Pskov region 67,82
61,81
74,05
29
The Republic of Mordovia 70,56
64,79
76,39
71
Kemerovo Region 67,72
61,50
74,04
30
Kaliningrad region 70,51
65,10
75,68
72
Sakhalin Oblast 67,70
62,17
73,53
31
Ulyanovsk region 70,50
64,64
76,30
73
Novgorod region 67,67
60,89
74,75
32
Murmansk region 70,46
65,15
75,26
74
The Republic of Buryatia 67,67
62,32
73,06
33
Yaroslavl region 70,45
64,25
76,37
75
Altai Republic 67,34
61,48
73,44
34
Leningrad region 70,36
64,73
76,05
76
Magadan Region 67,12
61,84
72,77
35
Tomsk Oblast 70,33
64,78
75,90
77
Transbaikal region 67,11
61,47
73,10
36
Kirov region 70,26
64,31
76,29
78
Irkutsk region 66,72
60,32
73,28
37
Oryol Region 70,22
64,36
75,92
79
Amur region 66,38
60,59
72,59
38
Novosibirsk region 70,19
64,29
76,13
80
Nenets autobrog 65,76
60,22
75,21
39
Arkhangelsk region 70,16
64,11
76,27
81
Jewish Autonomous Region 64,94
58,84
71,66
40
Kursk Oblast 70,14
64,27
76,00
82
Chukotsky autobrog 62,11
58,65
66,42
41
Kaluga region 70,02
64,43
75,51
83
Tyva Republic 61,79
56,37
67,51
42
Udmurtia 69,92
63,52
76,33
Note: Not taken into account Crimea and Sevastopol, included in the Russian Federation in 2014
Russia and world
Video: Life expectancy in the world, 2014
Table: UN Rating on the expected life expectancy of the population
Rating Country both husband. wives. m.
rankg.
rank1
Japan 83,7
80,5
86,8
7
1
2
Switzerland 83,1
80,0
86,1
1
6
3
Singapore 83,0
80,0
85,0
10
2
4
Australia 82,8
80,9
84,8
3
7
5
Spain 82,8
80,1
85,5
9
3
6
Iceland 82,7
81,2
84,1
2
10
7
Italy 82,7
80,5
84,8
6
8
8
Israel 82,5
80,6
84,3
5
9
9
France 82,4
79,4
85,4
4
5
10
Sweden 82,4
80,7
84,0
16
12
Table: Russia in the UN ranking
106
Kyrgyzstan 71,1
67,2
75,1
111
102
107
Egypt 70,9
68,8
73,2
100
111
108
Bolivia 70,7
68,2
73,3
103
110
109
DPRK. 70,6
67,0
74,0
113
108
110
Russia 70,5
64,7
76,3
127
89
111
Kazakhstan 70,5
65,7
74,7
123
106
112
Belize 70,1
67,5
73,1
110
114
113
Fiji 69,9
67,0
73,1
114
115
114
Butane 69,8
69,5
70,1
97
126
115
Tajikistan 69,7
66,6
73,6
116
109
Perspectives on life expectancy in the Russian Federation
Video: Average life expectancy in Russia
