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