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In this article, a new three-parameter asymmetric Laplace distribution and its extension are introduced. This includes as special case the symmetric Laplace double-exponential distribution. The distribution has established a direct link to estimation of quantile and quantile regression. Properties of the new distribution are presented. Application is made to a flood data modeling example. Keywords: Asymmetric Laplace distributionParameter estimationQuantile Acknowledgments We thank Dr. Alan Watkins and a referee for thoughtful comments which led to a substantial improvement of the article.
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Yu et al. (2005) studied this question.
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