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Maximum Likelihood Estimation of Asymmetric Laplace Parameters

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Abstract

Maximum likelihood estimators (MLE's) are presented for the parameters of a univariate asymmetric Laplace distribution for all possible situations related to known or unknown parameters. These estimators admit explicit form in all but two cases. In these exceptions effective algorithms for computing the estimators are provided. Asymptotic distributions of the estimators are given. The asymptotic normality and consistency of the MLE's for the scale and location parameters are derived directly via representations of the relevant random variables rather than from general sufficient conditions for asymptotic normality of the MLE's.

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Authors and Affiliations

  1. Department of Engineering Management and Systems Engineering, George Washington University, Washington, D.C, 20052, U.S.A

    Samuel Kotz

  2. Department of Mathematics, University of Nevada, Reno, NV, 89557-0045, U.S.A

    Tomasz J. Kozubowski

  3. Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, Indianapolis, IN, 46202, U.S.A

    Krzysztof Podgórski

Authors
  1. Samuel Kotz
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  2. Tomasz J. Kozubowski
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  3. Krzysztof Podgórski
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Kotz, S., Kozubowski, T.J. & Podgórski, K. Maximum Likelihood Estimation of Asymmetric Laplace Parameters. Annals of the Institute of Statistical Mathematics 54, 816–826 (2002). https://doi.org/10.1023/A:1022467519537

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  • DOI: https://doi.org/10.1023/A:1022467519537

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