A New Method for Generating Discrete Analogues of Continuous Distributions

In this paper we use discrete fractional calculus for showing the existence of delta and nabla discrete distributions and then apply time scales for definition of delta and nabla discrete gamma distributions. The main result of this paper is unification of the continuous and discrete gamma distribut...

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Bibliographic Details
Published in:Journal of statistical theory and applications 2018-03, Vol.17 (1), p.39-58
Main Authors: Ganji, M., Gharari, F.
Format: Article
Language:English
Subjects:
Discrete fractional calulus
Fractional calculus
Gamma distribution
Research Article
Time
Time scale
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Summary:In this paper we use discrete fractional calculus for showing the existence of delta and nabla discrete distributions and then apply time scales for definition of delta and nabla discrete gamma distributions. The main result of this paper is unification of the continuous and discrete gamma distributions, which is at the same time a distribution to so-called time scale. Also, starting from the Laplace transform on time scales, we develop concept of moment generating function for these distributions.
ISSN:1538-7887
2214-1766
1538-7887
DOI:10.2991/jsta.2018.17.1.4