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, Volume 13, Issue 1, pp 1–43 | Cite as

Families of distributions arising from distributions of order statistics

  • M. C. JonesEmail author
Article

Abstract

Consider starting from a symmetric distributionF on ℜ and generating a family of distributions from it by employing two parameters whose role is to introduce skewness and to vary tail weight. The proposal in this paper is a simple generalisation of the use of the collection of order statistic distributions associated withF for this purpose; an alternative derivation of this family of distributions is as the result of applying the inverse probability integral transformation to the beta distribution. General properties of the proposed family of distributions are explored. It is argued that two particular special cases are especially attractive because they appear to provide the most tractable instances of families with power and exponential tails; these are the skewt distribution and the logF distribution, respectively. Limited experience with fitting the distributions to data in their four-parameter form, with location and scale parameters added, is described, and hopes for their incorporation into complex modelling situations expressed. Extensions to the multivariate case and to ℜ+ are discussed, and links are forged between the distributions underlying the skewt and logF distributions and Tadikamalla and Johnson'sL U family.

Key words

Beta distribution LogF distribution LU distribution order statistics probability integral transform skewt distribution 

AMS

subject classification 60E05 62E10 62F99 

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Copyright information

© Sociedad Española de Estadística e Investigación Operativa 2004

Authors and Affiliations

  1. 1.Department of StatisticsThe Open UniversityMilton KeynesU.K.

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