The Journal of the Indian Mathematical Society

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Some Results for the Inverse Moment of the N-Fold Convolution of the Zero-Truncated Negative Binomial Distribution


Affiliations
1 Department of Mathematics, Shanghai University, Shanghai 200444, India
     

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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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  • Some Results for the Inverse Moment of the N-Fold Convolution of the Zero-Truncated Negative Binomial Distribution

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Authors

Feng-Zhen Zhao
Department of Mathematics, Shanghai University, Shanghai 200444, India

Abstract


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.

References