Displaying similar documents to “An inductive derivation of Stirling numbers of the second kind and their applications in statistics.”

k-th rekord values from Dagum distribution and characterization

Devendra Kumar (2016)

Discussiones Mathematicae Probability and Statistics

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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...

The recurrence relations for the moments of the discrete probability distributions

Tadeusz Gerstenkorn

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CONTENTS1. The presentation of the problem........................................................................................................ 51.1. Introduction.......................................................................................................................................... 51.2. The presentation of the known results........................................................................................... 52. The recurrence relations for the moments about...

On formulae for central moments of counting distributions

Katarzyna Steliga, Dominik Szynal (2015)

Applicationes Mathematicae

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The aim of this article is to give new formulae for central moments of the binomial, negative binomial, Poisson and logarithmic distributions. We show that they can also be derived from the known recurrence formulae for those moments. Central moments for distributions of the Panjer class are also studied. We expect our formulae to be useful in many applications.

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

Tadeusz Gerstenkorn (2004)

Open Mathematics

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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...

A note on the Polya-Eggenberger distributions with s=1 and some applications.

William C. Guenther (1981)

Trabajos de Estadística e Investigación Operativa

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Although cumulative probabilities for the Pólya-Eggenberger distributions can be easily found in modern computing facilities, the special cases s=1 can be handled with hypergeometric tables. Applications are mentioned.

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 ≥ 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...