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Some properties and applications of probability distributions based on MacDonald function
Applications of Mathematics, Tome 27 (1982) no. 4, pp. 285-302
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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 $x^nK_n(x), x\geq 0, \left|x\right|^n K_n(x\left|x\right|), x\in \bold R$ and $x^{n+1}K_n(x), x\geq 0$ 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.
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 $x^nK_n(x), x\geq 0, \left|x\right|^n K_n(x\left|x\right|), x\in \bold R$ and $x^{n+1}K_n(x), x\geq 0$ 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.
DOI : 10.21136/AM.1982.103973
Classification : 33A40, 33C10, 60E99, 62E15
Keywords: MacDonald function; Bessel function of the second kind; composed distributions 
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Kropáč, Oldřich. Some properties and applications of probability distributions based on MacDonald function. Applications of Mathematics, Tome 27 (1982) no. 4, pp. 285-302. doi: 10.21136/AM.1982.103973

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