Article
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Degenerate Poisson Distribution
Version 1
: Received: 19 August 2019 / Approved: 20 August 2019 / Online: 20 August 2019 (11:14:22 CEST)
How to cite: Duran, U.; Acikgoz, M. Degenerate Poisson Distribution. Preprints 2019, 2019080214. https://doi.org/10.20944/preprints201908.0214.v1 Duran, U.; Acikgoz, M. Degenerate Poisson Distribution. Preprints 2019, 2019080214. https://doi.org/10.20944/preprints201908.0214.v1
Abstract
The main purpose of this paper is to introduce and investigate degenerate Poisson distrib- ution which is a new extension of the Poisson distribution including the degenerate expo- nential function. We then provide several properties of the degenerate Poisson distribution such as the first and the second raw moments and di¤erence operator property. Moreover, we acquired the skewness and the kurtosis for the degenerate Poisson distribution. We also derive its moment generating function by which we define the degenerate Bell polynomials and give a connection for these polynomials related to the unsigned Stirling numbers of the
rst kind.
Keywords
Poisson distribution; raw moments; Bell polynomials; degenerate exponential function; unsigned Stirling number of the first kind.
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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