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.
Poisson distribution; raw moments; Bell polynomials; degenerate exponential function; unsigned Stirling number of the first kind.
MATHEMATICS & COMPUTER SCIENCE, Probability and Statistics
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