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A Family of Waiting time Distributions Arising from a Bivariate Bernoulli Scheme

Author

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  • H. M. Barakat

    (Faculty of Science, Zagazig University)

Abstract

A new univariate five-parameter generalized negative binomial distribution based on the bivariate Bernoulli scheme is introduced. This distribution produces a new three-parameter generalized geometric distribution in a natural manner using probabilistic properties of the four-outcome model. Some basic statistical properties of the new distribution are studied. In addition, estimation of the unknown parameters is illustrated. Moreover, a new univariate three-parameter generalized exponential distribution is derived as a limit of the proposed three-parameter generalized geometric distribution. Finally, a generalization of the proposed distributions based on trivariate Bernoulli scheme is introduced.

Suggested Citation

  • H. M. Barakat, 2019. "A Family of Waiting time Distributions Arising from a Bivariate Bernoulli Scheme," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(1), pages 213-224, March.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:1:d:10.1007_s13226-019-0319-6
    DOI: 10.1007/s13226-019-0319-6
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    References listed on IDEAS

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    1. H. Barakat, 2001. "The Asymptotic Distribution Theory of Bivariate Order Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 487-497, September.
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