A Class of Power Series <i>q</i>-Distributions

Abstract

A class of power series q-distributions, generated by considering a q-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its q-factorial moments are obtained in terms of q-derivatives of its series (parametric) function. Also, it is shown that the convolution of power series q-distributions is also a power series q-distribution. Furthermore, the q-Poisson (Heine and Euler), q-binomial of the first kind, negative q-binomial of the second kind, and q-logarithmic distributions are shown to be members of this class of distributions and their q-factorial moments are deduced. In addition, the convolution properties of these distributions are examined.

Keywords

• Euler distribution
• Heine distribution
• negative <i>q</i>-binomial distribution
• <i>q</i>-binomial distribution
• <i>q</i>-factorial moments
• <i>q</i>-logarithmic distribution