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Some Results for the Inverse Moment of the N-Fold Convolution of the Zero-Truncated Negative Binomial Distribution
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In this paper, we consider the r-th inverse moment of the n-fold convolution of the zero-truncated negative binomial distribution Gr(k; n). We mainly discuss the first and second inverse moments of this distribution. We derive some recursive formulas for Gr(k; n). In particular, we give some asymptotic approximations for the first and second inverse moments of the n-fold convolution of the zero-truncated negative binomial distribution.
Keywords
Negative Binomial Distribution, Inverse Moment, Recursive Formulas, Asymptotic Approximation.
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