On the degenerate negative λ-binomial and Poisson random variables from degenerate special polynomials

Abstract

In this paper, we investigate the theory and applications of negative lambda-binomial random variable with parameter $(r,p)$(r,p) and Poisson random variable with parameter $\alpha $alpha. In particular, we show that the expectation of rising factorial sequences or degenerate rising factorial sequences of negative lambda-binomial random variables or Poisson random variables are strongly related to Lah numbers, modified degenerate Lah-Bell polynomials, the Stirling numbers of the first kind and Bell polynomials.