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 article, we study sooner/later waiting time problems for simple patterns in a sequence of bivariate trials. The double generating functions of the sooner/later waiting times for the simple patterns are expressed in terms of the double generating functions of the numbers of occurrences of...

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>

Some of the methods of estimation of allele frequencies and inbreeding coefficients in a K-allele model are examined. A result that has long been assumed to be true is proved. That is, in the presence of inbreeding, the maximum likelihood estimators of the allele frequencies and of the...