Estimating the Parameters of a Certain Multivariate Exponential Distribution.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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The problem of parameter estimation for a k 1-parameter version of the k-dimensional multivariate exponential distribution MVE of Marshall and Olkin is investigated. Although this MVE is not absolutely continuous with respect to Lebesgue measure, a density with respect to a dominating measure is specified, enabling the derivation of a likelihood function and likelihood equations. In general, the likelihood equations are not solvable explicitly but are shown to have an unique root which is the maximum likelihood estimator MLE. A simple estimator INT is derived from intuitive considerations and also arises as the first iterate in a simple procedure to solve the likelihood equations iteratively. The sequence of estimators obtained by this procedure is shown to converge to the MLE for sufficiently large samples. Modified author abstract
- Statistics and Probability