PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION

Hai Yan XU;He Liang FEI

Journal of Systems Science & Complexity ›› 2005, Vol. 18 ›› Issue (1) : 86-094.

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PDF(116 KB)
Journal of Systems Science & Complexity ›› 2005, Vol. 18 ›› Issue (1) : 86-094.
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PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION

  • Hai Yan XU, He Liang FEI
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Abstract

Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the threshold parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered.

Key words

Exponential distribution / grouped data / maximum likelihood estimate (MLE) / asymptotic property / inte

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Hai Yan XU , He Liang FEI. PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION. Journal of Systems Science and Complexity, 2005, 18(1): 86-094
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