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Negative Moments of Positive Random Variables

M. T. Chao and W. E. Strawderman
Journal of the American Statistical Association
Vol. 67, No. 338 (Jun., 1972), pp. 429-431
DOI: 10.2307/2284399
Stable URL: http://www.jstor.org/stable/2284399
Page Count: 3
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Negative Moments of Positive Random Variables
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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.

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