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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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