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Statistics
A Journal of Theoretical and Applied Statistics
Volume 47, 2013 - Issue 3
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Original Articles

On the existence and uniqueness of the MLEs of the parameters of a general class of exponentiated distributions

, &
Pages 605-612 | Received 18 May 2011, Accepted 12 Aug 2011, Published online: 19 Sep 2011
 

Abstract

In this paper, we present a formal simple proof for the existence and uniqueness of the maximum likelihood estimates (MLEs) of the parameters of a general class of exponentiated distributions. This class includes the exponentiated (general) exponential, exponentiated Rayleigh (scaled Burr X) and exponentiated Pareto distributions, as special cases, and thus the proof given here establishes the existence and uniqueness of the MLEs for these important special cases as well.

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