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The L-distribution and skew generalizations

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  • Fischer, Matthias J.
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    Abstract

    Leptokurtic or platykurtic distributions can, for example, be generated by applying certain non-linear transformations to a Gaussian random variable. Within this work we focus on the class of so-called power transformations which are determined by their generator function. Examples are the H-transformation of Tukey (1960), the J-transformation of Fischer and Klein (2004) and the L-transformation which is derived from Johnson's inverse hyperbolic sine transformation. It is shown that generator functions themselves which meet certain requirements can be used to construct both probability densities and cumulative distribution functions. For the J-transformation, we recover the logistic distribution. Using the L-transformation, a new class of densities is derived, discussed and generalized. --

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    Bibliographic Info

    Paper provided by Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics in its series Discussion Papers with number 63/2004.

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    Date of creation: 2004
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    Handle: RePEc:zbw:faucse:632004

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    Web page: http://www.statistik.wiso.uni-erlangen.de/
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    Related research

    Keywords: Power kurtosis transformation; leptokurtosis; (skew) L-distribution;

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    1. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
    2. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "A Constructive Representation of Univariate Skewed Distributions," Econometrics 0403002, EconWPA.
    3. Rayner, G. D. & MacGillivray, H. L., 2002. "Weighted quantile-based estimation for a class of transformation distributions," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 401-433, June.
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