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Mortality statistics are generally compiled from death registrations (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 during his last illness, 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.
The course of mortality throughout life may be described by a mortality table 1 or life table 1. This consists of one or more life table functions 2, all of which are mathematically related and may generally be 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 exact age x, 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 or root 5 of the life table and the process of diminution is known as attrition 6. From a knowledge of the survivorship function it is possible to compute the probability of survival 7 from exact age x to exact age x+ n.
- 4. The number of survivors to exact age x is denoted by lx.
- 7. The probability of survival from age x to age x + n is always written npx and from age x to age x + 1: px.
The differences between the number of survivors (431-4) at different ages give the number of deaths within the age interval or the death function 1. The ratio of deaths between ages x and x + n to the number of survivors at age x is called the probability of death 2 between ages x and x+ n. The central death rate 3 is the ratio of deaths between ages x and x + n to the mean population alive at that age. The force of mortality 4 or instantaneous death rate 4 is the derivative of the natural logarithm of the survivorship function (431-3) taken negatively.
- 1. The number of deaths between ages x and x + n is written ndx and between ages x and x + 1 is written dx.
- 2. The probability of dying between age x and x + n is written nqx and between ages x and x + 1 is written qx.
- 3. The central death rate at age x is written mx.
- 4. The force of mortality at age x is written µx.
By integrating the survivorship function (431-3) between two given ages we obtain the total number of years lived 1 or total lifetime 1 of the cohort between these ages. By summing this function from a given age x to the end of life, we obtain the total number of years lived after attaining age x by those reaching this age, which is sometimes called the total after lifetime 2. This figure, divided by the number of survivors to age x, would then be called the mean after lifetime; it is the expectation of life 3 or life expectancy 3 at that age. The expectation of life at birth 4 is also called the mean length of life 4. The reciprocal of the expectation of life at birth is occasionally used as an index of mortality under the name of life table death rate 5. The expectation of life of an individual at age x is sometimes called his life potential 6 and the life potential of a population is the sum of the life potentials of its members.
- 1. The notation for the total number of years lived between ages x and x + n is nLx.
- 2. The notation for the total after lifetime at age x is Tx.
- 3. The notation for the expectation of life at age x is e°x.
The median length of life 1 (cf. 140-6) sometimes called the probable length of life 1 is the age at which half the original cohort (116-2) of births have died. After infancy the distribution of deaths by age in the life table (431-1) will usually have a mode (140-8) and the age corresponding to it 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 mean (433-4) or the probable length of life. The term life span 4 is sometimes used for the maximum possible length of human life.
A complete life table 1 is generally one in which the values of the life table functions (431-2) are given in single years of age. An abridged life table 2 is one in which the functions are given only for certain pivotal ages 3 and the intermediate values have to be obtained by interpolation (151-7). Occasionally the expression select life table 5 is used to denote a table relating to the experience of a number of specially selected individuals who have been chosen on grounds of health, in opposition to general life tables 6, sometimes called aggregate life tables 6 by actuaries.
A current life table 1 (cf. 153-2; 431-1) is one in which the mortality rates used relate to a specified time interval and the cohort (116-2) is therefore fictitious (cf. 153-3). A generation life table 2, or cohort life table 2 on the other hand, traces the experience of an actual cohort and the mortality rates contained therein are then spread over a prolonged period, usually about 100 years. A mortality surface 3 is drawn when age-specific death rates (401-7) are plotted against age and time period simultaneously in a three-dimensional diagram.
A method of computing life table functions (431-2) which is frequently employed in demography is based upon the Lexis diagram 1 in which every individual is represented by a life line 2 which begins at birth and ends in the point of death 3. This method makes use of a combined classification of deaths by age at death and year of birth. A method has recently been put forward to study mortality (401-1) at very advanced ages and has been called the method of extinct generations 4.
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