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Multilingual Demographic Dictionary, second unified edition, English volume
43
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430
Mortality statistics are generally compiled from death registration (cf. 211). When a death takes place a death certificate ^{1} is generally issued; statistics are compiled from the information given on death certificates. In some countries a distinction is made between the medical certificate of death ^{2} issued by a medical practitioner who has attended the deceased person at the time of his/her death, and an ordinary death certificate issued by the registrar of deaths for legal purposes.
- 1. The first death statistics in England and Wales were compiled from bills of mortality which were generally drawn up on the basis of burial registers. In countries where vital registration is deficient, statistics can be gathered by the survey technique; questions may be asked on deaths during a reference period, generally the previous year; the indirect estimation of mortality relies on such questions as the number of children surviving among children ever born (637-2), reporting of sibling deaths, orphanhood status or widowhood status.
431
Probabilities of dying ^{1} or death probabilities ^{1} are used to study in detail the mortality of a period or of a cohort. They are the probabilities that an individual of exact age x will die before exact age x + n, and are represented by the symbol _{n}q_{x}. If n = 1, we talk about annual death probabilities ^{2}; if n = 5, about quinquennial death probabilities ^{3}. The instantaneous death rate ^{4}, or as it is occasionally called the force of mortality ^{4}, is the limit of the _{n}q_{x} value as n tends to zero. The projective mortality probability ^{5★} is the probability that individuals of the same cohort or group of cohorts died between two January 1^{st}. The name of this probability comes from its use in the calculation of population projections. It is also equal to 1-L_{x+n}/L_{x}, where L_{x} is the person-years lived by the stationary population from exact age x to exact age x+n. The complement to one of the probability of dying from exact age x to exact age x + n is the probability of survival ^{6} over this interval. In the preparation of population projections, we use survival ratios ^{7}; they represent the probability that individuals of the same birth cohort or group of cohorts will still be alive n years later.
- 1. The probability of death between age x and x + n is defined as the ratio of deaths between ages x and x+n to the number of survivors at exact age x. It is not to be confused with the central death rate, the ratio of deaths between ages x and x+n to the mean population alive at that age. The central death rate is written _{n}m_{x} .
- 6. The probability of survival from age x to age x+n is written _{n}p_{x} .
- 7. A survival ratio is the complement to one of the projective mortality probability. Individuals in the cohorts do not have the same age and therefore are not at the same risk of dying.
432
The course of mortality throughout the life cycle may be described by a life table ^{1}. A life table consists of several life table functions ^{2}, all of which are mathematically related and may be generally derived when the value of one of them is known. The survivorship function ^{3} shows the number of survivors ^{4} of a cohort (116-2) of births to various exact ages (322-7) on the assumption that the cohort is subjected to the rates of mortality shown. The number of births in the original cohort is known as the radix ^{5} of the life table and the process by which the original cohort is reduced is known as attrition ^{6}.
- 4. The number of survivors to exact age x is denoted by l_{x} .
- 5. The radix is usually a power of 10: 10,000 or 100,000 for example.
433
To the survivors function corresponds a death function ^{1} which is calculated as the differences between the number of survivors (432-4) at different ages. It is named the distribution of life table deaths ^{2★} in order to be distinguished from the crude distribution of deaths. Life tables typically include the expectation of life ^{3} or life expectancy ^{3} at age x ; this is the mean number of years to be lived by those surviving to exact age x, given the mortality conditions of the table. The expectation of life at birth ^{4} is a particular case of expectation of life, and represents the mean length of life ^{4} of individuals who have been subjected since birth to the mortality of the table. The reciprocal of the expectation of life at birth is the life table death rate ^{5} or death rate of the stationary population ^{5}.
- 3. By integrating the survivorship function (432-3) between two exact given ages we obtain the total number of years lived by the cohort between these ages; the notation for the total number of years lived between age x and x + n is _{n}L_{x} . This function is often called the stationary population in life table column headings. By summing it from a given age x to the end of life, we obtain the total number of years to be lived after attaining age x by those reaching that age; the conventional notation is T _{x} .
- 4. The notation for the expectation of life at age x is e_{x}
434
The median length of life ^{1} sometimes called the probable length of life ^{1} is the age at which half the original cohort of births have died. After infancy the distribution of deaths by age in the life table will usually have a mode and the corresponding age is called the modal age at death ^{2}, or sometimes the normal age at death ^{2}. It may be of interest as an indicator of human longevity ^{3} or the length of life ^{3} corresponding more closely to the sense in which the term is used in everyday language than either the average (433-4) or the median length of life. The term life span ^{4} is used to refer to the maximum possible length of human life.
435
A complete life table ^{1} is usually one in which the values of the life table functions (432-2) are given in single years of age. An abridged life table ^{2} is one in which most functions are given only for certain pivotal ages, frequently spaced at five or ten year intervals after infancy; intermediate values for the functions are usually obtained by some form of interpolation (151-7). The term life table for selected heads ^{3} is used to refer to a life table relating to the experience of a number of specially selected individuals, such as the clients of a life insurance company, in opposition to general life tables ^{4} which relate the experience of a whole population (101-4). Life tables are generally presented on a sex-specific basis although on occasion they are presented for both sexes. A life table which is based only upon the generalization of empirical relationships is called a model life table ^{5}.
436
A calendar-year life table ^{1} or period life table ^{1} (cf. 153-2; 432-1) is one in which the mortality rates used relate to a specified time interval and the cohort (116-2) is therefore hypothetical. A generation life table ^{2}, or cohort life table ^{2} on the other hand, traces the experience of an actual birth cohort and the mortality rates contained in the table are then spread over a prolonged period, usually about 100 years. A mortality surface ^{3} is drawn when probabilities of dying (431-1) are plotted against age and time period simultaneously in a three-dimensional diagram.
437
The Lexis diagram ^{1} is commonly used to illustrate the usual method for computing death probabilities and other demographic measures. In this diagram, every individual is represented by a life line ^{2} which begins at birth and ends in the point of death ^{3}. A method for the study of mortality at very advanced ages has been called the method of extinct generations ^{4}, because it uses observed deaths for cohorts which have been completely eliminated by mortality.
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