다국어인구학사전, 두 번째 통합본, 한국어판

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430

Mortality statistics are generally compiled from death registration (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 or her 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. 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 question as the number of children surviving among children ever born (637-2), orphanhood status or widowhood status.

431

Probabilities of dying¹ or death probabilities¹ 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 _nq_x. If n = 1, we talk about annual death probabilities²; if n = 5, about quinquennial death probabilities³. The instantaneous death rate⁴, or as it is occasionally called the force of mortality⁴, is the limit of the _nq_x value as n tends to zero. The complement to one of the probability of dying from exact age x to exact age x + n is the probability of survival⁶ over this interval. In the preparation of population projections, we use survival ratios⁷; 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 _nm_x .
• 6. The probability of survival from age x to age x + n is written _np_x .

432

The course of mortality throughout the life cycle may be described by a life table¹. A life table consists of several life table functions², all of which are mathematically related and may be generally 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 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 radix⁵ of the life table and the process by which the original cohort is reduced is known as attrition⁶.

• 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

The differences between the number of survivors (432-4) at different ages gives the number of deaths within the given age interval of the death function¹. Life tables typically include the expectation of life³ or life expectancy³ 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 birth⁴ is a particular case of expectation of life, and represents the mean length of life⁴ 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 rate⁵ or death rate of the stationary population⁵.

• 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 _nL_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 life¹ sometimes called the probable length of life¹ 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 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 average (433-4) or the median length of life. The term life span⁴ is used to refer to the maximum possible length of human life.

435

A complete life table¹ is usually one in which the values of the life table functions (432-2) are given in single years of age. An abridged life table² 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 heads³ 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 tables⁴ 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 table⁵.

436

A calendar year life table¹ or period life table¹ (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 table², or cohort life table² 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 surface³ is drawn when probabilities of dying (431-1) are plotted against age and time period simultaneously in a three-dimensional diagram.

437

The Lexis diagram¹ 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 line² which begins at birth and ends in the point of death³. A method for the study of mortality at very advanced ages has been called the method of extinct generations⁴, because it uses observed deaths for cohorts which have been completely eliminated by mortality.