A Note on Inverse Moments of Binomial Variates

Inverse moments of univariate discrete distributions via the Poisson expansion

In this note we present a series expansion of inverse moments of a non-negative discrete random variate in terms of its factorial cumulants, based on the Poisson-Charlier expansion of a discrete distribution. We apply the general method to the positive binomial distribution and obtain a convergent series for its inverse moments with an error residual that is uniformly bounded on the entire inte...

Asymptotic Expansion for Inverse Moments of Binomial and Poisson Distributions

An asymptotic expansion for inverse moments of positive binomial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribution. Compared to previous results, a single expansion formula covers all (also non-integer) inverse moments. In addition, the approach can be generalized to other positive distributions.

Computer generation of negative binomial variates by envelope rejection

This paper proposes an envelope rejection method for computer sampling from the negative binomial distribution, with index parameter α and probability parameter p, based on a simple probability distribution inequality. Comparative timings with existing methods of generating NB variates show that the proposed method is comparable or faster when α is not too large (α < 11), and it is fastest for ...

Testing Equality of Proportion of Success of Several Correlated Binomial Variates

A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays

We study the properties of a parameterized family of generalized Pascal matrices, defined by Riordan arrays. In particular, we characterize the central elements of these lower triangular matrices, which are analogues of the central binomial coefficients. We then specialize to the value 2 of the parameter, and study the inverse of the matrix in question, and in particular we study the sequences ...