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Type II Binomial Distribution of Order k with Gaps

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Abstract

We introduce the Type II binomial distribution of order k with gap g and derive its double pgf in closed form. Expressions for the moments, the pgf, and the pmf as nested binomial sums are also derived. For the case \(g=2\), closed from expressions for the mean and variance are obtained. For \(g>2\), we derive closed form asymptotic expressions for all the moments (in addition to the full expressions as nested binomial sums mentioned above). We also correct some published results for \(g=1\).

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Funding

S. J. Dilworth was supported by the National Science Foundation under Grant Number DMS–1361461.

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    S. J. Dilworth

  2. Convergent Computing Inc., P.O. Box 561, Shoreham, NY, 11786, USA

    S. R. Mane

Authors
  1. S. J. Dilworth
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  2. S. R. Mane
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Correspondence to S. R. Mane.

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Dilworth, S.J., Mane, S.R. Type II Binomial Distribution of Order k with Gaps. J Indian Soc Probab Stat 19, 105–120 (2018). https://doi.org/10.1007/s41096-018-0037-0

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  • DOI: https://doi.org/10.1007/s41096-018-0037-0

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