Motivated by recent results by Nadarajah, Srivastava and Gupta (
2007
) in which the authors introduced a new formula for CDF F
K
of the McKay Bessel function distribution containing the modified ...Bessel function
we aim to present new formulae for F
K
, especially for certain values of parameters for which their formula fails to be calculated by in-built numerical routines. Also, several computational series formulae are obtained for the CDF of McKay Bessel distribution which contains modified Bessel function
one is given in terms of the Horn confluent hypergeometric function
and the others by Kampé de Fériet function
Marcum Q-function and modified Bessel functions
Horn confluent hypergeometric function
and finally in terms of incomplete Gamma function γ and Exton's double hypergeometric X-function.
The main aim of this article is to derive three new formulas for the cumulative distribution function of the noncentral chi-square distribution. The main advantage of such formulas is that they are ...given in terms of modified Bessel functions, leaky aquifer function and generalized incomplete gamma function which have a wide range of applications. In addition, the computational efficiency of the newly derived formulas versus already known formulas is established.
The main aim of this article is to establish a summation formula for the second type Neumann series which members contain a product of two modified Bessel functions of the first kind of not ...necessarily equal orders and arguments.
The first part of the article contains integral expressions for products of two Bessel functions of the first kind having either different integer orders or different arguments. A similar question ...for a product of modified Bessel functions of the first kind is solved next, when the input functions are of different integer orders and have different arguments.
The cumulative distribution function of the non-central chi-square distribution χn′2(λ) of n degrees of freedom possesses an integral representation. Here we rewrite this integral in terms of a lower ...incomplete gamma function applying two of the second mean-value theorems for definite integrals, which are of Bonnet type and Okamura’s variant of the du Bois–Reymond theorem. Related results are exposed concerning the small argument cases in cumulative distribution function (CDF) and their asymptotic behavior near the origin.
In this note our aim is to present some monotonicity properties of the product of modified Bessel functions of the first and second kind. Certain bounds for the product of modified Bessel functions ...of the first and second kind are also obtained. These bounds improve and extend known bounds for the product of modified Bessel functions of the first and second kind of order zero. A new Turán type inequality is also given for the product of modified Bessel functions, and some open problems are stated, which may be of interest for further research.
Motivated by certain current results by Pogány and Parmar
10
in which the authors introduced the so-called
p
-extended Mathieu series, the main aim of this paper is to present a connection between ...such series and various types of Schlömilch series.
Observations on the McKay Iν Bessel distribution Górska, Katarzyna; Horzela, Andrzej; Jankov Maširević, Dragana ...
Journal of mathematical analysis and applications,
12/2022, Letnik:
516, Številka:
1
Journal Article
Recenzirano
The main aim of this article is to derive new representation formulae for CDF of random variable distributed according to the McKay Iν Bessel law: first set of formulae are given in terms of ...incomplete generalized Fox–Wright function while the other expressions include Exton generalized hypergeometric X function of two variables, and also the incomplete Lipschitz–Hankel integral for the modified Bessel function of the first kind. Also we establish the connection between CDF of the McKay Iν Bessel rv and another important CDF which belongs to the non–central chi–square law. Another goal is to give answers to the moment determinacy problem, unimodality and some mode results for this distribution.
Observations on the McKay I Bessel distribution Górska, Katarzyna; Horzela, Andrzej; Jankov Maširević, Dragana ...
Journal of mathematical analysis and applications,
12/2022, Letnik:
516, Številka:
1
Journal Article
PDF
