On generating T-X family of distributions using quantile functions
The cumulative distribution function (CDF) of the T - X family is given by R { W ( F ( x ))}, where R is the CDF of a random variable T , F is the CDF of X and W is an increasing function defined on [0, 1] having the support of T as its range. This family provides a new method of generating univaria...
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Published in | Journal of statistical distributions and applications Vol. 1; no. 1; pp. 1 - 2 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
11.06.2014
Springer Nature B.V BioMed Central Ltd |
Subjects | |
Online Access | Get full text |
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Summary: | The cumulative distribution function (CDF) of the
T
-
X
family is given by
R
{
W
(
F
(
x
))}, where
R
is the CDF of a random variable
T
,
F
is the CDF of
X
and
W
is an increasing function defined on [0, 1] having the support of
T
as its range. This family provides a new method of generating univariate distributions. Different choices of the
R
,
F
and
W
functions naturally lead to different families of distributions. This paper proposes the use of quantile functions to define the
W
function. Some general properties of this
T
-
X
system of distributions are studied. It is shown that several existing methods of generating univariate continuous distributions can be derived using this
T
-
X
system. Three new distributions of the
T-X
family are derived, namely, the normal-Weibull based on the quantile of Cauchy distribution, normal-Weibull based on the quantile of logistic distribution, and Weibull-uniform based on the quantile of log-logistic distribution. Two real data sets are applied to illustrate the flexibility of the distributions. |
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ISSN: | 2195-5832 2195-5832 |
DOI: | 10.1186/2195-5832-1-2 |