Properties of the probability density function of the non-central chi-squared distribution

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:346

Article

Andras, Szilard²  Baricz, Arpad¹ 

[1] Univ Babes Bolyai, Fac Econ, RO-400591 Cluj Napoca, Romania

[2] Univ Babes Bolyai, Fac Math & Comp Sci, RO-400084 Cluj Napoca, Romania

关键词: non-central chi-squared distribution;    modified Bessel function;    Hoppe's formula;    Turan-type inequality;    monotone form of l'Hospital's rule;   

DOI  :  10.1016/j.jmaa.2008.05.074

来源: Elsevier

【 摘 要 】

In this paper we consider the probability density function (pdf) of a non-central chi(2) distribution with arbitrary number of degrees of freedom. For this function we prove that can be represented as a finite sum and we deduce a partial derivative formula. Moreover, we show that the pdf is log-concave when the degrees of freedom is greater or equal than 2. At the end of this paper we present some Turan-type inequalities for this function and an elegant application of the monotone form of l'Hospital's rule in probability theory is given. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free