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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Diskussionspapier ; No. 72/2006

Classification and Topics

• Classification: Wirtschaft

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Fischer, Matthias J.
• Event: Veröffentlichung
• (who): Friedrich-Alexander-Universität Erlangen-Nürnburg, Lehrstuhl für Statistik und Ökonometrie
• (where): Nürnberg
• (when): 2006

Further information

• Handle: http://hdl.handle.net/10419/29593
• Last update: 10.03.2025, 11:42 AM CET