期刊
RELIABILITY ENGINEERING & SYSTEM SAFETY
卷 91, 期 6, 页码 689-697出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.ress.2005.05.008
关键词
beta exponential distribution; kurtosis; Renyi entropy
The exponential distribution is perhaps the most widely applied statistical distribution for problems in reliability. In this note, we introduce a generalization-referred to as the beta exponential distribution-generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of the beta exponential distribution. We derive expressions for the moment generating function, characteristic function, the first four moments, variance, skewness, kurtosis, mean deviation about the mean, mean deviation about the median, Renyi entropy, Shannon entropy, the distribution of sums and ratios, and the asymptotic distribution of the extreme order statistics. We also discuss simulation issues, estimation by the methods of moments and maximum likelihood and provide an expression for the Fisher information matrix. We hope that this generalization will attract wider applicability in reliability. (c) 2005 Elsevier Ltd. All rights reserved.
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