Properties of the probability density function of the non-central chi-squared distribution |
| |
Authors: | Szilárd András |
| |
Institution: | a Babe?-Bolyai University, Faculty of Mathematics and Computer Science, RO-400084 Cluj-Napoca, Romania b Babe?-Bolyai University, Faculty of Economics, RO-400591 Cluj-Napoca, Romania |
| |
Abstract: | In this paper we consider the probability density function (pdf) of a non-central χ2 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 Turán-type inequalities for this function and an elegant application of the monotone form of l'Hospital's rule in probability theory is given. |
| |
Keywords: | Non-central chi-squared distribution Modified Bessel function Hoppe's formula Turá n-type inequality Monotone form of l'Hospital's rule |
本文献已被 ScienceDirect 等数据库收录! |