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...

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...

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 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...