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Some Identities based on Success Runs of at Least Length k

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  • Sonali Bhattacharya

    (Symbiosis Centre for Management and Human Resource Development, (Deemed University), India)

Abstract

In this research paper, an attempt has been made to obtain alternative formulas for distributions of order k based on runs of at least length k. First by using binomial scheme and ‘balls-into-cells’ technique an alternative formula for distribution of binomial distribution of order k as defined by Goldstein [1]. Inverse Bionomial scheme was then used with ‘ball-into-cells technique to obtain alternate distribution of Geometric distribution of order k and negative binomial distribution of order k. The results were further extended to obtain Polya-Eggenberger distribution of order k and Inverse Polya-Eggenberger distributions of order k. All results were verified for exactness of probability.

Suggested Citation

  • Sonali Bhattacharya, 2018. "Some Identities based on Success Runs of at Least Length k," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 4(2), pages 39-43, January.
    • Handle: RePEc:adp:jbboaj:v:4:y:2018:i:2:p:39-43
    DOI: 10.19080/BBOAJ.2018.04.555634
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    References listed on IDEAS

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    1. Sigeo Aki & Katuomi Hirano, 1996. "Lifetime distribution and estimation problems of consecutive-k-out-of-n:F systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(1), pages 185-199, March.
    2. Ling, K. D., 1989. "A new class of negative binomial distributions of order k," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 371-376, April.
    3. Ling, K. D., 1988. "On binomial distributions of order k," Statistics & Probability Letters, Elsevier, vol. 6(4), pages 247-250, March.
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