On the behaviour of the characteristic function of a probability distribution in the neighbourhood of the origin

Author:

Pitman E. J. G.

Abstract

Let X be a real valued random variable with probability measure P and distribution function F. It will be convenient to take F as the intermediate distribution function defined by . In mathematical analysis it is a little more convenient to use this function rather than , which arise more naturally in probability theory. In all cases we shall consider With this definition, if the distribution function of X is F(x), then the distribution function of −X is 1−F(−x). The distribution of X is symmetrical about 0 if F(x) = 1 − F(−x).

Publisher

Cambridge University Press (CUP)

Reference5 articles.

1. Some theorems on characteristic functions of probability distributions;Pitman;Proc. Fourth Berkeley Symp. Math. Statist. Prob.,1960

2. Sur un mode de croissance régulière. Théorèmes fondamentaux

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