Summary The intervened Poisson distribution (IPD) of Shanmugam (Biometrics 41:1025–1029, <CitationRef CitationID="CR19">1985</CitationRef>) has been found suitable for some rare event situations where some intervention arises. The main drawback of IPD is that it is under-dispersed and appropriate for single intervention situation....</citationref>

In this paper we develop an order k version of the alternative hyper-Poisson distribution of Kumar and Nair (Statistica, 2012) and study some of its important properties such as its probability mass function, first moment, variance and recurrence relations for its probabilities, raw moments and...

In this paper, we introduce a class of a directed acyclic graph on the assumption that the collection of random variables indexed by the vertices has a Markov property. We present a flexible approach for the study of the exact distributions of runs and scans on the directed acyclic graph by...

In this note we are concerned with the inflated-parameter binomial distribution, which is a generalization of the classical binomial distribution. We show that there exists exactly one renewal process such that the number of renewals has an inflated-parameter binomial distribution.

In this paper, recursive equations for waiting time distributions of r-th occurrence of a compound pattern are studied via the finite Markov chain imbedding technique under overlapping and non-overlapping counting schemes in sequences of independent and identically distributed (i.i.d.) or Markov...

A new general method for generating discrete random variables is presented. The method is based on reducing the problem of generating a discrete random variable with an extremely large range to that of generating a random variable with a small range consisting of a few possible values...

Consider an infinite sequence of Bernoulli trials {Xi|i=1,2,…}. Let W(k) denote the waiting time, the number of trials needed, to get either consecutive k ones or k zeros for the first time. The probability distribution of W(k) is derived for both independent and homogeneous two-state...