Negative Moments of Positive Random Variables
- 1 June 1972
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 67 (338) , 429
- https://doi.org/10.2307/2284399
Abstract
We investigate the problem of finding the expected value of functions of a random variable X of the form f(X) = (X+A)−n where X+A>0 a.s. and n is a non-negative integer. The technique is to successively integrate the probability generating function and is suggested by the well-known result that successive differentiation leads to the positive moments. The technique is applied to the problem of finding E[1/(X+A)] for the binomial and Poisson distributions.Keywords
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