The distribution of the longest run under binomial sampling
Date
1988
Authors
Majumder, Ajit Kumar
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Abstract
Assume that we have a sequence of N independent repeated Bernoulli trials with outcomes success(+ ) or failure(-) on each trial, where p = Pr(+ ) and q = Pr(- ) is the same for all trials. In this thesis we consider the distribution of R +, the length of the longest run of + signs, and of R, the length of the longest run of either + or - signs. A brief history of the general theory of runs is given in Chapter 1. In Chapter 2 we develop the theory for the distribution of the numbers of runs of +ve signs and of -ve signs, and for the total number of runs. Using similar methods, expressions for the distributions of R and of R+ are developed in Chapter 3 . Extensive tables of these distributions, and some related measures, are given in Appendix A . In Chapter 4 we describe the tables, give examples of their use, and give some details of the computational method. In appendix B and C we list the FORTRAN programs that were used to compute the tables.