Reply to “On ‘a new look at entropy and the life table’” by S. Mitra
Bibliographic Data
| ID | 10967625 |
|---|---|
| Authors | N Goldman (0000-0003-2865-9491, Office of Population Research, 21 Prospect Avenue, Princeton, New Jersey 08544, corresponding author), GRAHAM LORD (Mathtech, Carnegie Center, Princeton, New Jersey 08540), Graham M Lord (0000-0003-2069-4743) |
| Year | 1987 |
| Volume | 24 |
| Issue | 3 |
| Pages | 441-442 |
| Publication date | 1987-08-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Demography (JOURNAL) |
| Journal identifiers | ISSN: 0070-3370 • E-ISSN: 1533-7790 |
| Publisher | Duke University Press (PUBLISHER • US) |
| DOI | 10.2307/2061310 |
| OpenAlex | W2086035680 |
| Language | EN |
| Citations received | 1 |
| References cited | 6 |
Derivations by Mitre were made on the approximation of H in quantifying the alteration in life expectancy due to sudden mortality change as employed by Keyfitz in short note on the Taeuber paradox. The author replies to these formulations and takes new look at entropy and the life table and discusses some implications. The example is given that Mitre set up values for H which exceeded unity in the Coale and Demeny West Life Tables; this was done after previously published work identified that H was bounded by 1. The position in this paper is that H cannot exceed 1. An alternative approximation of mortality changes on the expectation of life is provided. This new formula gives the average number of years person can expect to live given 2nd chance on life relative to the expected life span. Mitre used similar formula but only in his development of the approximation of H. The finiteness of H is deduced solely from the property that life expectancy tends to zero as a approaches the oldest age of life w which is finite. The author defines H according to McClean which is different from the subsequent work of Demetrius. Demetrius implies that H is less than 1 if a the mean age of the stationary population is less than the expectation of life at birth. The limit behavior is insufficient by itself to force the boundness of H if w is taken to equal infinity. It is necessary that life expectancy tend to zero as a approaches infinity for the convergence of the integral in the numerator. The authors characterization of life tables exhibiting an H value larger than 1 is based on 2 families of curves for modeling all or part of the survival function. The 1st family of curves claims that the limit behavior does not mimic human life table but that it is possible to have H larger than 1 for specific value of k which is less than or equal to 1. The 2nd family of curves also provides the simplicity of the functional form of the family which clarifies the relationship of life at x to its derivative functions and to H
Bounded function · Combinatorics · Econometrics · Entropy (arrow of time · Infinity · Life expectancy · Life span · Life table · Mathematical analysis · Mathematical economics · Physics · Population · Sociology · Demography · Insurance, Mortality, Demography, Risk Management · Mathematics · Medicine · Gerontology
| Citations per year | 0.04 |
|---|---|
| Citation span | 1998 - 1998 (1) |
| Highly cited | No |