The true maximum-likelihood estimators for the generalized Gaussian distribution with p = 3, 4, 5 |
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Authors: | Rui Li Saralees Nadarajah |
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Affiliation: | School of Mathematics, University of Manchester, Manchester, UK |
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Abstract: | The generalized Gaussian distribution with location parameter μ, scale parameter σ, and shape parameter p contains the Laplace, normal, and uniform distributions as particular cases for p = 1, 2, +∞, respectively. Derivations of the true maximum-likelihood estimators of μ and σ for these special cases are popular exercises in many university courses. Here, we show how the true maximum-likelihood estimators of μ and σ can be derived for p = 3, 4, 5. The derivations involve solving of quadratic, cubic, and quartic equations. |
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Keywords: | Cubic equation quadratic equation quartic equation |
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