Characterization Problems Associated with the Exponential Distribution - Brossura

Azlarov, T. A. A.; Volodin, N. A.

Brossura

ISBN 10: 146129374X ISBN 13: 9781461293743

Casa editrice: Springer, 2011

Riassunto

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.

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Contenuti

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.

Product Description

Book by Azlarov T A Volodin N A

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 146129374X
• ISBN 13: 9781461293743
• Rilegatura: Copertina flessibile
• Numero di pagine: 148
• Redattore: Olkin I.
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania