Families of distributions arising from distributions of order statistics

By M. Chris Jones. 2004

502 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0b48e619bb8b5ec2c093d4afe29eea83f1d440d8

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Citations in the corpus

On families of beta- and generalized gamma-generated distributions and associated inference (2009, methodology): “One such example is a broad family of univariate distributions generated from the beta distribution, proposed by Jones [1] (see also [2]), which extends the original beta family of distributions with the incorporation of two additional parameters.”
On Families of Distributions with Shape Parameters (2015, unknown): “The beta distribution is a natural two-parameter choice; this was ﬁrst published by Eugene, Lee & Famoye (2002) when g = φ and applied to general g in Jones (2004) — where, admittedly, this view of the family was secondary to one based on order statistics which has since proved less popular.”
A Generalization of the Skew-Normal Distribution: The Beta Skew-Normal (2011, methodology): “We denote this distribution Beta skew-normal (BSN) since it is a special case of the Beta generated distribution (Jones (2004)).”
Log-gamma-generated families of distributions (2014, methodology): “Jones [11] considered Equation (5) as a family of distributions motivated by the distribution of order statistics and studied its distributional properties in general as well as its potential for exciting statistical applications.”
The beta log-logistic distribution (2014, unknown): “Recent developments focus on new techniques for building meaningful distributions, including the two-piece approach introduced by Hansen (1994) and the generator approach pioneered by Eugene et al. (2002) and Jones (2004).”
Two-sided generalized Topp and Leone (TS-GTL) distributions (2008, background): “Jones [6] recently investigated the generalizations of the distribution of order statistics of the form {B(a, b)}−1f (x)F a−1(x){1 − F(x)}b−1, (8) where as usual B(a, b) = (a + b)/ (a) (b), F(·) is a particular cdf and a, b > 0 are not necessarily the integers.”
Construction of multivariate distributions: a review of some recent results (2008, methodology): “…i = 1,2, . . . , p. 6 Construction of multivariate distributions: a review of some recent results In the univariate case, family (2) becomes gF(x) = Γ(a1 + a2) Γ(a1)Γ(a2) f (x)Fa1−1(x)[1 − F(x)]a2−1, (5) which was also proposed by Jones (2004) and it is a generalization of the r-order statistics.”
Closed-form expressions for moments of a class of beta generalized distributions (2011, background): “the Lauricella function of type A [Exton (1978); Aarts (2000)] defined by”
A generalization of the exponential-Poisson distribution (2008, methodology): “Applications using two real data sets ar presented. keywords: Exponential-Poisson distribution, Generalized exponential-Poisson distribution, Failure rate, Order statistics, Fisher’s information matrix.”