A New Approach to the Poisson Distribution: Degenerate Poisson Distribution

Abstract

The main purpose of this paper is to introduce and investigate degenerate Poisson distribution which is a new extension of the Poisson distribution including the degenerate exponential function. We then provide several properties of the degenerate Poisson distribution such as the first and the second raw moments and difference 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 first kind.