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Statistical Distributions in Scientific Work pp 189–195Cite as

On the Moments and Factorial Moments of a MPSD

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Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 79))

Summary

In this paper we present a general method of obtaining the moment generating function and hence the moments of a Modified Series distribution introduced by Gupta (1974). The factorial moments are also obtained as by-products. These results are then employed to derive the moments and factorial moments of the generalized negative binomial, the generalized Poisson, the generalized logarithmic series, and the lost game distributions. Some of the well-known results follow trivially.

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References

  • Amidi, A. (1978). A note on the moments of the generalized negative binomial distribution and on certain properties of this distribution. SIAM Journal on Applied Mathematics, 34, 223–224.

    Article  MathSciNet  MATH  Google Scholar 

  • Comtet, L. (1974). Advanced Combinatorics.. Reidel, New York.

    MATH  Google Scholar 

  • Gupta, R. C. (1974). Modified power series distribution and some of its applications. Sankhya, Series B, 35, 288–298.

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  • Gupta, R. C. (1975). Maximum likelihood estimation of modified power series distribution and some of its applications. Communications in, Statistics, 4, 689–697.

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  • Gupta, R. C. (1977). Minimum variance unbiased estimation in a modified power series distribution and some of its applications. Communications in Statistics A, 6, 977–991.

    Article  Google Scholar 

  • Gupta, R. C. and Singh, J. (1980). Estimation of probabilities in the class of modified power series distributions, (to appear).

    Google Scholar 

  • Haight, F. A. and Breuer, M. A. (1960). The Borel-Tanner distribution. Biometrika, 47, 143–146.

    MathSciNet  MATH  Google Scholar 

  • Kemp, A. W. and Kemp, C. D. (1968). On a distribution associated with certain Stochastic processes. Journal of Royal Statistical Society, Series B, 30, 160–163.

    MathSciNet  Google Scholar 

  • Patel, J. K., Kapadia, C. H., and Owen, D. B. (1976). Handbook of Statistical Distributions. Marcel Dekker, New York.

    MATH  Google Scholar 

  • Riorden, J. (1968). combinatorial Identities. Wiley, New York.

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of Maine at Orono, Orono, Maine, 04469, USA

    Pushpa Lata Gupta

  2. Temple University, Philadelphia, Pennsylvania, 19122, USA

    Jagbir Singh

Authors
  1. Pushpa Lata Gupta
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  2. Jagbir Singh
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Editor information

Editors and Affiliations

  1. Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania, USA

    Charles Taillie  & Ganapati P. Patil  & 

  2. Instituto di Calcolo delle Probabilità, Facoltà di Scienze Statistische Demografiche e Attuariali, Università degli Studi di Roma, Italy

    Bruno A. Baldessari

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© 1981 D. Reidel Publishing Company

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Gupta, P.L., Singh, J. (1981). On the Moments and Factorial Moments of a MPSD. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8549-0_15

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  • DOI: https://doi.org/10.1007/978-94-009-8549-0_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-8551-3

  • Online ISBN: 978-94-009-8549-0

  • eBook Packages: Springer Book Archive

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