On the existence and uniqueness of the MLEs of the parameters of a general class of exponentiated distributions |
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| Authors: | M. E. Ghitany R. A. Al-Jarallah N. Balakrishnan |
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| Affiliation: | 1. Department of Statistics and Operations Research, Faculty of Science , Kuwait University , Kuwait meghitany@yahoo.com;3. Department of Statistics and Operations Research, Faculty of Science , Kuwait University , Kuwait;4. Department of Mathematics and Statistics , McMaster University , Hamilton , Ontario , Canada |
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| 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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| Keywords: | exponentiated exponential distribution exponentiated Rayleigh distribution Burr X distribution exponentiated Pareto distribution maximum likelihood estimates |
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