Characterization Problems Associated with the Exponential Distribution

ISBN-13: 9781461293743 / Angielski / Miękka / 2011 / 137 str.

T. A. Azlarov; N. A. Volodin; I. Olkin

Opis

Problems of calculating the reliability of instruments and systems and the development of measures to increase efficiency and reduce operational costs confronted physicists and mathe- maticians at the end of the '40's and the beginning of the '50's in connection with the unrelia- bility of electro-vacuum instruments used in aviation. Since then steadily increasing demands for the accuracy, reliability and complexity required in electronic equipment have served as a stimulus in the development of the theory of reliability. From 1950 to 1955 Epstein and Sobel 67,68] and Davis 62], in an analysis of statistical data of the operating time of an instrument up to failure, showed that the distribution is exponential in many cases. Consequently, the ex- ponential distribution became basic to research associated with experiments on life expectancy. Further research has shown that there are a whole series of problems in reliability theory for which the exponential distribution is inapplicable. However, it can practically always be used as a first approximation. The ease of computational work due to the nice properties of the exponential distribution (for example, the lack of memory property, see Section 1) is also a reason for its frequent use. AB a rule, data on the behavior of the failure rate function are used to test the hypothesis that a given distribution belongs to the class of exponential distributions, and order statistics are used to estimate the parameter of the exponential distribution.

Spis treści

1 Introduction.- 1.1 Characterization of the exponential distribution by the lack of memory property.- 2 Characterization Problems in the Class of Distributions with a Monotone Failure Rate.- 3 Some Properties of Order Statistics.- 4 Characterization of the Exponential Distribution by an Independent Function of its Order Statistics.- 5 Characterization of the Exponential Distribution by a Property of its Order Statistics.- 6 Characterizations of the Distributions by Moment Properties of Order Statistics.- 7 Characterization Problems of the Geometric Distribution.- 8 Characterization of the Exponential Distribution using the Geometric Distribution.- 9 Multivariate Exponential Distributions and their Characterizations.- Comments.- Author Index.