Type II Binomial Distribution of Order k with Gaps

  • S. J. Dilworth
  • S. R. Mane
Research Article


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 \(g=1\).


Type II binomial distribution Bernoulli trials Gaps between success runs 

Mathematics Subject Classification

primary 62E15 secondary 60E05 



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


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Copyright information

© The Indian Society for Probability and Statistics (ISPS) 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.Convergent Computing Inc.ShorehamUSA

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