calculation OF INDICATORS
The population at the beginning of the year is obtained by adding the number of live births, persons who have arrived and immigrants during theyear to the population at the beginning of the year , and subtracting the number of deaths, persons who have departed and emigrants during the year :
,
where:
– year;
– the population at the beginning of the year ;
– the population at the beginning of the year ;
– the number of live births during the year ;
– the number of persons who have arrived and immigrants during the year ;
– the number of deaths during the year ;
– the number of persons who have departed and emigrants during the year .
Average annual population is the average population in the age interval in a respective year :
,
where:
– year;
– the age of the population ( = 0, 1, 2, …);
– the length of the age interval;
– the population in the age interval at the beginning of the year ;
– the population in the age interval at the beginning of the year +1.
Total age dependency ratio is the number of children under 15 and elderly persons (aged 65 and older) per 100 population aged 15–64 at the beginning of the respective year :
,
where:
– year;
– the population aged 0–14 at the beginning of the year ;
– the population aged 15–64 at the beginning of the year ;
– the population aged 65 and older at the beginning of the year .
Young age dependency ratio is the number of children under 15 per 100 population aged 15–64 at the beginning of the year :
,
where:
– year;
– the population aged 0–14 at the beginning of the year ;
– the population aged 15–64 at the beginning of the year .
Index of ageing is the population aged 65 and older per 100 children aged under 15 at the beginning of the year :
,
where:
– year;
– the population aged 0–14 at the beginning of year ;
– the population aged 65 and older at the beginning of the year .
Age-specific fertility rate defines the fertility rate in the year t by women’s age groups of [15–20), [20–25), ..., [45–50). The fertility rate for the group at the age of in the year is expressed per mille and defined:
where:
– year;
– women’s age ( = 15, 16, ..., 49);
– the length of the age interval ( = 1, 2, 3, …); if = 1, then the age interval length is 1; if = 5, then the age interval length is 5;
– the number of live births in the women’s age interval in the year ;
– the average annual number of women in the age interval in the year .
Total fertility rateis an indicator showing the average number of children who would be born alive to a woman during the reproductive period of her life if she were to bear children in accordance with the current age-specific fertility rate.
where:
– year;
– women’s age ( = 15, 16, ..., 49);
– the age-specific fertility rate in the mothers’ age (a one-year interval is taken) in the year .
A woman’s reproductive age is the woman’s 15–49year age period.
Gross reproduction rate is the average number of daughters that would be born alive to a woman during her lifetime if she were to pass through her childbearing years conforming to age-specific fertility rates of the year .
,
where:
– year;
– women’s age ( = 15, 16, ..., 49);
– the proportion of female infants in the total number of live births;
– the age-specific fertility rate in the mothers’ age (a one-year interval is taken) in the year .
Net reproduction rate is the average number of daughters that would be born alive to a woman during her lifetime if she were to pass through her childbearing years conforming to age-specific fertility and mortality rates by age of the year .
,
where:
– year;
– woman’s age ( = 15, 16, ..., 49);
– the proportion of female infants in the total number of live births;
– the age-specific fertility rate in the mothers’ age (a one-year interval is taken) in the year .
– the hypothetical number of live births, called radical and equal to 100 000;
– the number of person-years lived by women of the age (from the mortality table).
Mean age of women at childbirthin a given year:
,
where:
– year;
– women’s age ( = 15, 16, ..., 49);
– the age-specific fertility rate in the mothers’ age (a one-year interval is taken) in the year .
The mean age ofwomen at the birth of the first child in the year t:
,
where:
– year;
– women’s age ( = 15, 16, ..., 49);
– the age-specific fertility rate of first births in the age (a one-year interval is taken) in the year .
Infant mortality rate refers to a rate measuring infant mortality (infant deaths per 1000 live births) in the year t.
,
where:
– year;
– the number of infant deaths and live births during the year ;
– the number of infant deaths during the year and live births during the year –1;
– the number of live births during the year .
Perinatal mortality rate refers to a rate measuring perinatal mortality (stillbirths and infant deaths during the first week of life per 1000 live births and stillbirths) in the year t.
,
where:
– year;
– the number of infant deaths during the first week of life in the year t;
– the number of stillbirths in the year t;
– the number of live births in the year t.
Life expectancy at birth is calculated by compiling the mortality tables which are based on the estimation of the probability to attain a certain age. Therefore, prior to calculating the life expectancy at birth, certain additional indicators are calculated:
The mortality rate of an age group is smoothed by calculating the geometric mean of 3 elements:
,(1)
where
– age ( = 15, 16, 17, …);
– age interval length (n = 1, 2, 3, …).
The last age group is not smoothed. To prevent deviations from the exact number of deaths, a ratio between the actual and smoothed number of deaths needs to be calculated. The ratio obtained is multiplied by the smoothed mortality indicator within the age group.
The average number of years lived by persons who have died by age group:
The average number of years lived by persons who have died within the zero age group:
,
where:
– number of infants who have died at age, where – days, weeks, months;
– share of time lived in regard to (, if – days, , if – weeks, , if – months).
The average number of years lived by persons who have died within the 1–4 years old age group:
,
where:
– number of children who have died at age within the age group;
– share of time lived in regard to within the age group.
The average number of years lived by persons who have died within other age groups:
.
The average number of years lived by persons who have died within the last age group is not calculated.
The probability of dying within the age group:
,(2)
where:
– age ( = 0, 1, 2, …);
– age interval length (n = 1, 2, 3, …);
– average number of years lived within the age interval by persons who have died within this age interval.
– smoothed mortality indicator within the age group calculated by (1).
Within the last age group.
The probability to live from toage:
,(3)
Where – the probability to die within the age group calculated by (2).
Within the last age group.
Number of persons aged :
or , (4)
where:
– age ( = 0, 1, 2, …);
– age interval length (n = 1, 2, 3, …);
– number of persons who have lived to years;
– hypothetical number of live births (equals 100 000);
– probability to live from to years calculated by (3);
– probability to die within the age group calculated by (2).
Number of persons who have died within the age group :
or ,
where:
– age ( = 0, 1, 2, …);
– age interval length (n = 1, 2, 3, …);
– number of persons who have lived to years, calculated by (4);
– the probability of dying within the age group calculated by (2).
Within the last age group.
Number of years of persons alive within the age group :
,(5)
where:
– age ( = 0, 1, 2, …);
– age interval length (n = 1, 2, 3, …);
– number of persons who have lived to years calculated by (4);
– average number of years lived within the age interval by persons who have died within this age interval.
Within the last age group.
The total number of years lived by persons who were alive after they were aged:
,(6)
where:
– number of years of persons alive within the age group calculated by (5).
Within the last age group.
Life expectancy at birth of persons aged x:
,
where:
– the total number of years lived by persons who were alive after they were aged calculated by (6);
– number of persons who have lived to years.