A Stochastic Study of the Life Table and Its Applications: I. Probability Distributions of the Biometric Functions

Variance models of the last age interval and their impact on life expectancy at subnational scales

“…The hypothetical use of true LE variances would therefore tend to further increase the impact of the estimated LE variance corrections and thus further strengthen the conclusions the study. Overall, the 'corrected' LE variance formulae derived in this study account for the stochastic contribution of agespecific death counts according to established statistical theory (Brillinger 1986;Chiang 1960;Keyfitz 1966), and thus are expected to be reasonable estimates of the true LE variance.…”

“…However, it is also a statistical estimator that is computed from underlying random variables: the vital statistics of deaths and births (Brillinger 1986;Chiang 1960) as well as population counts. Each LE estimate thus has a statistical variance that represents a measure of its precision: this precision can be expressed as a standard error, coefficient of variation, or confidence interval, for example.…”

“…Assessment of LE variance is especially pertinent to smaller, subnational populations 5 , where variability in LE can become substantial. Chiang (Chiang 1960(Chiang , 1984 first provided a detailed assessment of the statistical properties of life tables and LE. He derived the only analytic equation for the variance of LE, which he expressed, using the delta method, as a weighted sum of the variances of the underlying age-specific survival probabilities.…”

Nonparametric predictive inference with right-censored data

“…The data were given by Freireich, et al [34]. The data are on survival of 42 patients with acute leukemia, recruited to a randomized trial aimed at assessing the ability of ,7) 0.0480 (6,7) 0.0480 0.8157 0.8636 (7,10) 0.0480 (7,10) (7,9) 0.0510 0.7677 0.8157 (9,10) 0.0030 (7,10) (9,10) 0.7647 (10,13) 0.0546 (10,13) (10,11) 0.0588 0.7101 0.7647 (11,13 0.0042 (11,13) 0.7059 (13,16) 0.0588 (13,16) 0.0588 0.6470 0.7059 (16,22) 0.0588 (16,22) (16,17) 0.0809 0.5882 0.6470 (17,22) 0.0059 (17,19) 0.5823 (19,22) 0.0072 (19,20) 0.5751 (20,22) 0.0090 (20,22) We are interested in the remission time of a future patient undergoing Control A …”

Some examples of double exponential fitness functions

“…The first two of these suffer from the disadvantage of not necessarily producing fitness estimates in the range (0, 1) while the third has the disadvantage that the relationship between the selection time and the parameters of the function is far from simple. (Chiang, 1960).…”