Some inference problems related to geometric distribution

Abstract

Reliability analysis is the branch of statistics that deals with collection of data, modeling and analysis of data on lifetimes of units or equipments. The area in which statistics has had its greatest impact in reliability is in the analysis of laboratory and field data on lifetimes or failure times. Statisticians have perhaps concentrated too much in literature on statistical niceties for certain distributions, and too little on innovative methods of life data analysis. Also a large amount of additional research has concerned continuous as opposed to discrete lifetimes. However, discrete lifetimes have important applications. Actuaries and bio-statisticians are interested in the lifetimes of persons or organisms, measured in months, weeks or days. For reliability engineers, time can also be the number of times that a piece of equipment is operated, or the number of miles that a tyre is used. There is a strong case for looking at reliability aspects in the discrete domain. The geometric distribution, owing to its lack of memory property and constant failure rate, is widely used to model discrete lifetimes. Motivated by the relevance and usefulness of the geometric model, this research aims to obtain some results that have applications in the modeling and analysis of data in the discrete time domain. This thesis is divided into 6 chapters. Chapter 1 serves as an introduction, which proposes a survey of literature relating to the subject matter of our present study, the basic definitions and notations used in the thesis and finally an outline of the work planned. As the geometric model belongs to the class of long tailed distributions, the occurrence of extreme observations is quite common and their identification as outliers or not becomes important. In Chapter 2, procedures for the determination of the number of outliers present in the sample taken from geometric distribution are discussed.