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Asymmetric Laplace Distributions

In: The Laplace Distribution and Generalizations

Author

Listed:
  • Samuel Kotz

    (George Washington University, Department of Engineering Management and Systems Engineering)

  • Tomaz J. Kozubowski

    (University of Nevada, Department of Mathematics)

  • Krzysztof Podgórski

    (Indiana University—Purdue University, Department of Mathematical Sciences)

Abstract

Chapter 3 is devoted to asymmetric Laplace distributions — a skewed family of distributions that in our opinion is the most appropriate skewed generalization of the classical Laplace law. In the last several decades, various forms of skewed Laplace distributions have sporadically appeared in the literature. One of the earliest is due to McGill (1962), who considers distributions with p.d.f. 3.0.1 $$ f(x) = \left\{ {\begin{array}{*{20}c} {\frac{{\varphi _1 }} {2}e^{ - \varphi _1 |x - \theta |} , x \leqslant \theta ,} \\ {\frac{{\varphi _2 }} {2}e^{ - \varphi _2 |x - \theta |} , x > \theta ,} \\ \end{array} } \right. $$ while Holla and Bhattacharya (1968) study the distribution with p.d.f. 3.0.2 $$ f(x) = \left\{ {\begin{array}{*{20}c} {p\varphi e^{ - \varphi \left| {x - \theta } \right|} , x \leqslant \theta ,} \\ {(1 - p)\varphi e^{ - \varphi \left| {x - \theta } \right|} , \theta

Suggested Citation

  • Samuel Kotz & Tomaz J. Kozubowski & Krzysztof Podgórski, 2001. "Asymmetric Laplace Distributions," Springer Books, in: The Laplace Distribution and Generalizations, chapter 3, pages 133-178, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0173-1_3
    DOI: 10.1007/978-1-4612-0173-1_3
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