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Generalized Tukey-type distributions with application to financial and teletraffic data

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  • Fischer, Matthias J.

Abstract

Constructing skew and heavy-tailed distributions by transforming a standard normal variable goes back to Tukey (1977) and was extended and formalized by Hoaglin (1983) and Martinez & Iglewicz (1984). Applications of Tukey's GH distribution family - which are composed by a skewness transformation G and a kurtosis transformation H - can be found, for instance, in financial, environmental or medical statistics. Recently, alternative transformations emerged in the literature. Rayner & MacGillivray (2002b) discuss the GK distributions, where Tukey's H-transformation is replaced by another kurtosis transformation K. Similarly, Fischer & Klein (2004) advocate the J-transformation which also produces heavy tails but - in contrast to Tukey's H-transformation - still guarantees the existence of all moments. Within this work we present a very general kurtosis transformation which nests H-, K- and J-transformation and, hence, permits to discriminate between them. Applications to financial and teletraffic data are given.

Suggested Citation

  • Fischer, Matthias J., 2006. "Generalized Tukey-type distributions with application to financial and teletraffic data," Discussion Papers 72/2006, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
  • Handle: RePEc:zbw:faucse:722006
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    1. Kabir K. Dutta & David F. Babbel, 2005. "Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions," The Journal of Business, University of Chicago Press, vol. 78(3), pages 841-870, May.
    2. Badrinath, S G & Chatterjee, Sangit, 1988. "On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index," The Journal of Business, University of Chicago Press, vol. 61(4), pages 451-472, October.
    3. Ingo Klein & Matthias Fischer, 2006. "Power kurtosis transformations: Definition, properties and ordering," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(3), pages 395-401, September.
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