Some properties and applications of probability distributions based on MacDonald function

Oldřich Kropáč

Aplikace matematiky (1982)

  • Volume: 27, Issue: 4, page 285-302
  • ISSN: 0862-7940

Abstract

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In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types x n K n ( x ) , x ≥ 0 , x n K n ( x x ) , x ∈ 𝐑 and x n + 1 K n ( x ) , x ≥ 0 are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and useful applications may be found in the field of non-Gaussian random processes, the marginal and joint probability densities of which and of their envelopes may be described by means of the types discussed.

How to cite

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Kropáč, Oldřich. "Some properties and applications of probability distributions based on MacDonald function." Aplikace matematiky 27.4 (1982): 285-302. <http://eudml.org/doc/15249>.

@article{Kropáč1982,
abstract = {In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types $x^nK_n(x), x\ge 0, \left|x\right|^n K_n(x\left|x\right|), x\in \mathbf \{R\}$ and $x^\{n+1\}K_n(x), x\ge 0$ are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and useful applications may be found in the field of non-Gaussian random processes, the marginal and joint probability densities of which and of their envelopes may be described by means of the types discussed.},
author = {Kropáč, Oldřich},
journal = {Aplikace matematiky},
keywords = {MacDonald function; Bessel function of the second kind; composed distributions; MacDonald function; Bessel function of the second kind; composed distributions},
language = {eng},
number = {4},
pages = {285-302},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some properties and applications of probability distributions based on MacDonald function},
url = {http://eudml.org/doc/15249},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Kropáč, Oldřich
TI - Some properties and applications of probability distributions based on MacDonald function
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 4
SP - 285
EP - 302
AB - In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types $x^nK_n(x), x\ge 0, \left|x\right|^n K_n(x\left|x\right|), x\in \mathbf {R}$ and $x^{n+1}K_n(x), x\ge 0$ are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and useful applications may be found in the field of non-Gaussian random processes, the marginal and joint probability densities of which and of their envelopes may be described by means of the types discussed.
LA - eng
KW - MacDonald function; Bessel function of the second kind; composed distributions; MacDonald function; Bessel function of the second kind; composed distributions
UR - http://eudml.org/doc/15249
ER -

References

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