Distribution characterization in a practical moment problem.

Jimbo, H.C.

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k-th rekord values from Dagum distribution and characterization

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In this study, we gave some new explicit expressions and recurrence relations satisfied by single and product moments of k-th lower record values from Dagum distribution. Next we show that the result for the record values from the Dagum distribution can be derived from our result as special case. Further, using a recurrence relation for single moments and conditional expectation of record values we obtain characterization of Dagum distribution. In addition, we use the established explicit...

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Oldřich Kropáč (1972)

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A compound of the generalized negative binomial distribution with the generalized beta distribution

Tadeusz Gerstenkorn (2004)

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This paper presents a compound of the generalized negative binomial distribution with the generalized beta distribution. In the introductory part of the paper, we provide a chronological overview of recent developments in the compounding of distributions, including the Polish results. Then, in addition to presenting the probability function of the compound generalized negative binomial-generalized beta distribution, we present special cases as well as factorial and crude moments of some...

Some properties and applications of probability distributions based on MacDonald function

Oldřich Kropáč (1982)

Aplikace matematiky

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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 $x^{n} K_{n} (x), x \geq 0, {|x|}^{n} K_{n} (x |x|), x \in 𝐑$ 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...