The central limit theorem and limit theorems for rarity require measures of normality and exponentiality for their implementation. Simple useful measures are exhibited for these in a metric space setting, obtained from inequalities for scale mixtures and power mixtures. It is shown that the Pearson coefficient of Kurtosis is such a measure for normality in a broad class $\mathscr{D}$ containing most of the classical distributions as well as the passage time densities $s_{mn}(\tau)$ for arbitrary birth-death processes.
Publié le : 1974-02-14
Classification:
Mixtures of distributions,
moment inequalities,
measures of exponentiality and normality,
birth-death processes,
weak convergence,
log-concavity,
log-convexity,
completely monotone densities,
total positivity,
sojourn times,
60E05,
60F05,
60J80
@article{1176996756,
author = {Keilson, Julian and Steutel, F. W.},
title = {Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and Normality},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 112-130},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996756}
}
Keilson, Julian; Steutel, F. W. Mixtures of Distributions, Moment Inequalities and Measures of Exponentiality and Normality. Ann. Probab., Tome 2 (1974) no. 6, pp. 112-130. http://gdmltest.u-ga.fr/item/1176996756/