Recurrence Relations for the Inverse Moments of the Positive Binomial Variable

Abstract

Grab and Savage [2] have obtained a recurrence formula for the first inverse moment of the positive binomial variable. In the present paper recurrence formula for the kth inverse moment of the positive binomial variable is derived, for k = 1, 2, …. The cumulative rounding error propagated by using these formulae recurrently is considered. Bounds for the propagated relative rounding error are obtained. By comparing some of the moments evaluated by the use of recurrence formulae, with the true values, it is noted that the rounding error involved in the first two inverse moments will be at most one unit in the last decimal place and the error will be practically zero when p is large.