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 λ-binomial random variable with parameter [Formula: see text] and Poisson random variable with parameter [Formula: see text]. In particular, we show that the expectation of rising factorial sequences or degenerate rising factorial sequences of negative λ-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.

Keywords

• negative λ-binomial random variable with parameter (r,p)
• Poisson random variable with parameters (r,p)
• degenerate bell polynomials