Families of distributions arising from distributions of order statistics
 M. C. Jones
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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 fourparameter 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.
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 Title
 Families of distributions arising from distributions of order statistics
 Journal

Test
Volume 13, Issue 1 , pp 143
 Cover Date
 20040601
 DOI
 10.1007/BF02602999
 Print ISSN
 11330686
 Online ISSN
 18638260
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Beta distribution
 LogF distribution
 L U distribution
 order statistics
 probability integral transform
 skewt distribution
 subject classification
 60E05
 62E10
 62F99
 Industry Sectors
 Authors

 M. C. Jones ^{(1)}
 Author Affiliations

 1. Department of Statistics, The Open University, Walton Hall, MK7 6AA, Milton Keynes, U.K.