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Estimating the Parameters of a Multivariate Exponential Distribution

Frank Proschan and Pasquale Sullo
Journal of the American Statistical Association
Vol. 71, No. 354 (Jun., 1976), pp. 465-472
DOI: 10.2307/2285335
Stable URL: http://www.jstor.org/stable/2285335
Page Count: 8
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Estimating the Parameters of a Multivariate Exponential Distribution
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Abstract

Parameter estimation for a (k + 1)-parameter version of the k-dimensional multivariate exponential distribution (MVE) of Marshall and Olkin is investigated. Although not absolutely continuous with respect to Lebesgue measure, a density with respect to a dominating measure is specified, enabling derivation of a likelihood function and likelihood equations. In general, the likelihood equations, not solvable explicitly, have a unique root which is the maximum likelihood estimator (MLE). A simple estimator (INT) is derived as the first iterate in solving the likelihood equations iteratively. The resulting sequence of estimators converges to the MLE for sufficiently large samples. These results can be extended to the more general (2k - 1)-parameter MVE.

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