On A Generalization Of Ling’S Binomial Distribution

Year 2013, Volume: 6 Issue: 3, 110 - 115, 31.12.2013

Femin Yalcin

Abstract

: In a sequence of n binary trials, distribution of the random variable M_n,k, denoting the
number of overlapping success runs of length exactly k, is called Ling’s binomial distribution or Type II
binomial distribution of order k. In this paper, we generalize Ling’s binomial distribution to Ling’s q-binomial
distribution using Bernoulli trials with a geometrically varying success probability. An expression for the
probability mass function of this distribution is derived. For q = 1, this distribution reduces to Ling’s binomial
distribution. 

Keywords

Binomial distribution of order k, Ling’s binomial distribution, q-distributions, runs

References

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