Revision as of 19:19, 7 November 2009

430

Mortality statistics are generally compiled from death registrations (cf. 211-). When a death takes place a death certificate¹ 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 death² 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.

431

The course of mortality throughout life may be described by a mortality table¹ or life table¹. This consists of one or more life table functions², all of which are mathematically related and may generally be derived when the value of one of them is known. The survivorship function³ shows the number of survivors⁴ 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 radix⁵ or root⁵ of the life table and the process of diminution is known as attrition⁶. From a knowledge of the survivorship function it is possible to compute the probability of survival⁷ from exact age x to exact age x+ n.

• 4. The number of survivors to exact age x is denoted by l_x.
• 7. The probability of survival from age x to age x + n is always written _np_x and from age x to age x + 1: p_x.

432

The differences between the number of survivors (431-.4) at different ages give the number of deaths within the age interval or the death function¹. The ratio of deaths between ages x and x + n to the number of survivors at age x is called the probability of death² between ages x and x+ n. The central death rate³ is the ratio of deaths between ages x and x + n to the mean population alive at that age. The force of mortality⁴ or instantaneous death rate⁴ 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 _nd_x and between ages x and x + 1 is written d_x.
• 2. The probability of dying between age x and x + n is written _nq_x and between ages x and x + 1 is written q_x.
• 3. The central death rate at age x is written m_x.
• 4. The force of mortality at age x is written µ_x.

433

By integrating the survivorship function (431-.3) between two given ages we obtain the total number of years lived¹ or total lifetime¹ 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 lifetime². This figure, divided by the number of survivors to age x, would then be called the mean after lifetime; it is the expectation of life³ or life expectancy³ at that age. The expectation of life at birth⁴ is also called the mean length of life⁴. The reciprocal of the expectation of life at birth is occasionally used as an index of mortality under the name of life table death rate⁵. The expectation of life of an individual at age x is sometimes called his life potential⁶ 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 _nL_x.
• 2. The notation for the total after lifetime at age x is T_x.
• 3. The notation for the expectation of life at age x is e°_x.

434

The median length of life¹ (cf. 140-.6) sometimes called the probable length of life¹ 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 death², or sometimes the normal age at death². It may be of interest as an indicator of human longevity³ or the length of life³ 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 span⁴ is sometimes used for the maximum possible length of human life.

435

A complete life table¹ is generally one in which the values of the life table functions (431-.2) are given in single years of age. An abridged life table² is one in which the functions are given only for certain pivotal ages³ and the intermediate values have to be obtained by interpolation (151-.7). Occasionally the expression select life table⁵ 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 tables⁶, sometimes called aggregate life tables⁶ by actuaries.

436

A current life table¹ (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 table², or cohort life table² 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 surface³ is drawn when age-specific death rates (401-.7) are plotted against age and time period simultaneously in a three-dimensional diagram.

437

A method of computing life table functions (431-.2) which is frequently employed in demography is based upon the Lexis diagram¹ in which every individual is represented by a life line² which begins at birth and ends in the point of death³. 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 generations⁴.

* * *