Abstract

A simple, accurate method of life table construction is advanced based upon a new way to estimate Chiang’s nax (the average number of years lived in the x to x + n age interval by those dying in the interval). The estimate for nax leads immediately to an expression for lx+n (the survivors to age x + n) in terms of lx and the known mortality rates for the interval x to x+n and the two adjacent intervals. The complete solution for the basic life table is given. The proposed method and five other easily applied methods are then compared against the standard provided by the U.S. life tables for 1969–1971. The results attest to the excellent performance and high degree of accuracy of the proposed method. Finally, extensions of the method to multiple decrement and associated single decrement life tables are briefly described.

This content is only available as a PDF.

References

Chiang, Chin-Long (
1960
).
A Stochastic Study of the Life Table and Its Applications, II: Sample Variance of the Observed Expectation of Life and Other Biometric Functions
.
Human Biology
,
32
,
221
238
.
Chiang, Chin-Long (
1968
).
Introduction to Stochastic Processes in Biostatistics
.
New York
:
John Wiley and Sons
.
Chiang, Chin-Long (
1972
).
On Constructing Current Life Tables
.
Journal of the American Statistical Association
,
67
,
538
541
. 10.2307/2284435
Chiang, Chin-Long, F. D. Norris, F. Olsen, P. W. Shipley, and H. E. Supplee. 1961. Determination of the Fraction of the Last Year of Life and Its Variation by Age, Race, and Sex. Unpublished manuscript presented at the American Public Health Association annual meeting in Detroit.
Fergany, N. (
1971
).
On the Human Survivorship Function and Life Table Construction
.
Demography
,
8
,
331
334
. 10.2307/2060621
Greville, T. N. E. (
1943
).
Short Methods of Constructing Abridged Life Tables
.
Record of the American Institute of Actuaries
,
32
(
Part 1
),
29
42
.
Greville, T. N. E. (
1948
).
Mortality Tables Analyzed by Cause of Death
.
Record of the American Institute of Actuaries
,
37
,
283
294
.
Jordan, Chester W. (
1967
).
Life Contingencies
. 2d. ed
Chicago
:
Society of Actuaries
.
Keyfitz, Nathan (
1968
).
A Life Table That Agrees With the Data: II
.
Journal of the American Statistical Association
,
63
,
1253
1268
. 10.2307/2285882
Keyfitz, Nathan (
1970
).
Finding Probabilities From Observed Rates, Or How to Make a Life Table
.
American Statistician
,
24
,
28
33
. 10.2307/2682293
Keyfitz, Nathan (
1977
).
Introduction to the Mathematics of Population
. Rev. ed.
Reading, Mass.
:
AddisonWesley Publishing Company
.
Keyfitz, Nathan, & Frauenthal, J. (
1975
).
An Improved Life Table Method
.
Biometrics
,
21
,
889
899
. 10.2307/2529814
Keyfitz, Nathan, & Flieger, W. (
1968
).
World Population: An Analysis of Vital Data
.
Chicago
:
University of Chicago Press
.
Mitra, S. (
1972
).
Comment on N. Fergany’s “On the Human Survivorship Function and Life Table Construction
.
Demography
,
9
,
515
515
. 10.2307/2060872
Preston, Samuel H., Keyfitz, N., & Schoen, R. (
1972
).
Causes of Death: Life Tables for National Populations
.
New York
:
Seminar Press
.
Preston, Samuel H., Keyfitz, N., & Schoen, R. (
1973
).
Cause-ofDeath Life Tables: Application of a New Technique to Worldwide Data
.
Transactions of the Society of Actuaries
,
25
,
83
109
.
Reed, L. J., & Merrell, M. (
1939
).
A Short Method for Constructing an Abridged Life Table
.
American Journal of Hygiene
,
30
,
33
62
.
Schoen, Robert (
1975
).
Constructing IncrementDecrement Life Tables
.
Demography
,
12
,
313
324
. 10.2307/2060768
Schoen, Robert, & Land, K. C. (
1977
).
A General Algorithm for Estimating a Markov-Generated IncrementDecrement Life Table With Applications to Marital Status Patterns
.
Urbana
:
Department of Sociology, University of Illinois at Urbana-Champaign
.
Shyrock, Henry S., Siegel, J. S., & Associates, (
1973
).
The Methods and Materials of Demography
. Rev. ed.
Washington, D.C.
:
U.S. Bureau of the Census (U.S. Government Printing Office)
.
Census of Population 1960. Vol. I: Characteristics of the Population. Part I, U.S. Summary
. (
1963
).
Washington, D.C.
:
U.S. Government Printing Office
.
United States Life Tables: 1959-61
. (
1964
).
Washington, D.C.
:
U.S. Government Printing Office
.
Methodology of the National Regional, and State Life Tables for the U.S.: 195961. Vol. I, No.4 by T. N. E. Greville
. (
1967
).
Washington, D.C.
:
U.S. Government Printing Office
.
United States Life Tables: 1969-71. Vol. I, No.1
. (
1975
).
Washington, D.C.
:
U.S. Government Printing Office
.
Methodology of the National and State Life Tables for the United States: 1969-71. Vol. 1, No.3
. (
1975
).
Washington, D.C.
:
U.S. Government Printing Office
.