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The true maximum-likelihood estimators for the generalized Gaussian distribution with p = 3, 4, 5

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  • Rui Li
  • Saralees Nadarajah

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.

Suggested Citation

  • Rui Li & Saralees Nadarajah, 2017. "The true maximum-likelihood estimators for the generalized Gaussian distribution with p = 3, 4, 5," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 8821-8835, September.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:18:p:8821-8835
    DOI: 10.1080/03610926.2016.1185121
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