Positive Linear Operators Generated by Analytic Functions

A new compounding family of distributions: The generalized gamma power series distributions

“…The coefficients a n 's depend only on n and C (θ ) =  ∞ n=1 a n θ n (for θ > 0) is assumed finite. It is important to remark that the probability class of distributions (3) has been considered in [19,20]. Table 1 lists some power series distributions (truncated at zero) defined by (3) such as the Poisson, logarithmic, geometric and binomial distributions.…”

“…Table 4 lists the first five moments of X obtained from Eqs. ( 12) and (19) for some parameter values.…”

Positive linear operators and summability

“…The problem of determining a sequence of points {x nk } corresponding to a given matrix A = (a nk (x)) such that the resulting operator defined by equation 1is convergent for each / in a certain class of functions is another matter and no results in this direction are given here. Some results of this type for operators generated by certain classes of analytic functions may be found in the paper of Boehme and Powell [2].…”