Bias in q and m rate estimates

Bias in estimates of the initial decremental rate q and the central decremental rate m is considered for several survival functions. It is first shown that the central rate estimate is unbiased when the survival function is an exponential curve; is similarly unbiased when the survival function assumes the Balducci shape. The evidence presented here also indicates that the proportional bias (the bias divided by the true value) is approximately twice as great for as for when the survival function is a straight line.Life tables in common use in the United Kingdom are, however, concave at ages arising most frequently in actuarial calculations, while none of the above curves is concave. In order to investigate the bias properties of general survival functions a quadratic is chosen, with a parameter indicating the extent of curvature. For this particular class of survival functions, one can show that bias is approximately minimized when exposure to risk is symmetric about the middle of the rate year.

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On Causes of Death in Britain (1970-72)

Transactions of the Faculty of Actuaries ◽

10.1017/s007136860000834x ◽

1977 ◽

Vol 36 ◽

pp. 53-68

Author(s):

J. J. McCutcheon

Keyword(s):

United Kingdom ◽

Causes Of Death ◽

Life Tables ◽

Relative Significance ◽

The United Kingdom ◽

Underlying Causes

The purpose of this paper is to analyse briefly the relative significance of the principal causes of death which currently prevail in the United Kingdom. The work is a sequel to that of references and, in which various life tables were produced from the data of the 1971 U.K. census and the numbers of deaths during the years 1970 to 1972. These earlier papers, however, study mortality without reference to the underlying causes of death.

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APPROXIMATION OF SURVIVAL FUNCTION FOR HETEROGENEOUS POPULATIONS

Scientific Journal of the Military University of Land Forces ◽

10.5604/01.3001.0002.3286 ◽

2011 ◽

Vol 162 (4) ◽

pp. 342-358

Author(s):

Stanisława OSTASIEWICZ

Keyword(s):

Survival Time ◽

Survival Function ◽

Polish Population ◽

Survival Functions ◽

Heterogeneous Populations ◽

Long Time ◽

General Survival

For a long time demographers and actuaries have been deliberating the issue of the laws of life. A number of proposed survival functions turned out to be unsatisfactory when they were applied empirically. One of the ways to overcome the difficulties is to modify the general survival functions by introducing an additional formula characterizing the frailty of individuals. Another way is to use a mixture of appropriate distributions. In this contribution the latter approach to determine the survival time of men in the Polish population in 2009 is applied.

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The Mortality Experience of Scotland in the Years 1930–32

Transactions of the Faculty of Actuaries ◽

10.1017/s0071368600002639 ◽

1938 ◽

Vol 16 (1) ◽

pp. 67-112

Author(s):

James Gray Kyd ◽

Peter Gordon Brown

Keyword(s):

United Kingdom ◽

Marital Status ◽

Life Tables ◽

Reliable Index ◽

Death Rates ◽

Mortality Experience ◽

The United Kingdom ◽

True Meaning ◽

National Life ◽

The Mean

SynopsisThe authors review the Life Tables published in connection with the 1931 Census of Scotland.They discuss the suitability of the enumerated population as a reliable index of the mean population to which deaths in the three calendar years nearest to the census date should be related, and explain the steps which were taken to obtain a more satisfactory representation of the true exposed to risk at periods of life when the census population was obviously unsuitable.The methods used for the graduation of the crude data are explained. Comparisons are made of the mortality of the two sexes and in regard to varying marital status. Further figures are given showing the relation between the mortality shown by the more recent tables and that exhibited by earlier investigations. The mortality in various parts of Scotland is exhibited and the death-rates in the country as a whole are compared with those found in other parts of the United Kingdom.The question of the most suitable function for use in comparing national life tables is considered and the popular misconception of the true meaning of the “expectation of life” is discussed.

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