Analysis of runs and patterns and their applications

Abstract

Abstract: A run or pattern is a specified sequence of outcomes that may occur at some point in a series of trials. The probabilistic analysis of runs and patterns plays an important role in many statistical areas. We will look at how runs and patterns arise from applied sciences such as reliability of engineering systems, DNA sequencing and nonparametric statistics. The probability of occurrence of a success run and other statistics like the mean waiting time for the first occurrence, mean and variance of the number of occurrences are obtained. We then look at success-failure runs and discuss how to obtain the mean and variance of the number of occurrences. We also obtain expression for the distance between occurrences of success-failure runs. We will also derive the probability of occurrence of a spaced pattern and study some asymptotic results for approximating the probability of occurrence of a spaced pattern.