On generating T-X family of distributions using quantile functions

Al‐Jarrah, Mohammad; Lee, Carl; Famoye, Felix

doi:10.1186/2195-5832-1-2

Cited by 132 publications

(138 citation statements)

References 35 publications

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“…Following the method of T-R{Y} family by Aljarrah et al (2014), we derive a generalization of Weibull distribution. Different families can be developed based on the choice of the quantile function of the random variable Y.…”

Section: Discussionmentioning

confidence: 99%

“…Normal-Weibull distribution (Aljarrah et al, 2014) and Gumbel-Weibull distribution (Al-Aqtash et al, 2014) are members of this family.…”

Section: B) T-weibull{exponential}mentioning

confidence: 99%

“…W function defined on the CDF () Fx by applying any two existing univariate distributions based on this method. Aljarrah et al (2014) extended the T-X family by defining (.) W in (1.4) as a quantile function of an existing random variable Y.…”

Section: Introductionmentioning

confidence: 99%

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Some Generalized Families of Weibull Distribution: Properties and Applications

AlMheidat¹,

Famoye²,

Lee³

2015

IJSP

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The Weibull distribution has been applied in various fields, especially to fit life time data. Some of these applications are limited partly due to the fact that the distribution has monotonically increasing, monotonically decreasing or constant hazard rate. This limitation undoubtedly inspired researchers to develop generalized Weibull distribution that can exhibit unimodal or bathtub hazard rate. In this article, we introduce six new families of T-Weibull{Y} distributions arising from the quantile function of a random variable Y. These six families are: The T-Weibull{uniform}, T-Weibull{exponential}, T-Weibull{log-logistic}, T-Weibull{Fré chet}, T-Weibull{logistic} and T-Weibull{extreme value}. Some properties of these families are discussed and general expressions for the quantile function, the Shannon's entropy, the non-central moments and the mean deviations are provided. Different new members of the T-Weibull{Y} families are derived and some of their properties are discussed. Two real data sets are used to illustrate the potential usefulness of the T-Weibull{Y} distributions and the results are compared with the results from some existing distributions.

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Section: Discussionmentioning

confidence: 99%

“…Normal-Weibull distribution (Aljarrah et al, 2014) and Gumbel-Weibull distribution (Al-Aqtash et al, 2014) are members of this family.…”

Section: B) T-weibull{exponential}mentioning

confidence: 99%

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Some Generalized Families of Weibull Distribution: Properties and Applications

AlMheidat¹,

Famoye²,

Lee³

2015

IJSP

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“…The generalization of the gamma distribution provides more flexible distributions for these different applications. This article applies the T -R{Y } framework proposed by Aljarrah et al (2014) to define T -gamma{Y } family by using the gamma random variable. Some general properties of the family are studied.…”

Section: Discussionmentioning

confidence: 99%

“…The T -R{Y } framework defined in Aljarrah et al (2014) (see also Alzaatreh et al, 2014b) is briefly described in the following. Let T , R and Y be random variables with CDF…”

Section: The T -Gamma{y } Family Of Distributionsmentioning

confidence: 99%

Family of generalized gamma distributions: Properties and applications

Alzaatreh¹,

Lee

Famoye

2015

HJMS

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In this paper, a family of generalized gamma distributions, T -gamma family, has been proposed using the T -R{Y } framework. The family of distributions is generated using the quantile functions of uniform, exponential, log logistic, logistic and extreme value distributions. Several general properties of the T -gamma family are studied in details including moments, mean deviations, mode and Shannon's entropy. Three new generalizations of the gamma distribution which are members of the T -gamma family are developed and studied. The distributions in the T -gamma family are very flexible due to their various shapes. The distributions can be symmetric, skewed to the right, skewed to the left, or bimodal. Four data sets with various shapes are fitted by using members of the T -gamma family of distributions.

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Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

Vasconcelos

Cintra

Nascimento

2021

Math Methods in App Sciences

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In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fréchet and Kumaraswamy distributions, and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fréchet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling's T 2 statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.

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On generating T-X family of distributions using quantile functions

Cited by 132 publications

References 35 publications

Some Generalized Families of Weibull Distribution: Properties and Applications

Some Generalized Families of Weibull Distribution: Properties and Applications

Family of generalized gamma distributions: Properties and applications

Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

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