Family of generalized gamma distributions: Properties and applications

Alzaatreh, Ayman; Lee, Carl; Famoye, Felix

doi:10.15672/hjms.20156610980

Cited by 19 publications

(22 citation statements)

References 35 publications

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“…This data set contains the time to failure (10 3 h) of turbocharger of a type of engine from Xu et al (2003). These data were studied by Alzaatreh et al (2016) and Cordeiro et al (2019) using Weibull-gamma {log-logistic} and odd Lomax-Lomax distributions, respectively. For this data set, we fit E-L {GW}, EEL, PRHL, GG, and TEV models.…”

Section: Turbocharger Datamentioning

confidence: 99%

Generalized logistic distribution and its regression model

2020

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A new generalized asymmetric logistic distribution is defined. In some cases, existing three parameter distributions provide poor fit to heavy tailed data sets. The proposed new distribution consists of only three parameters and is shown to fit a much wider range of heavy left and right tailed data when compared with various existing distributions. The new generalized distribution has logistic, maximum and minimum Gumbel distributions as sub-models. Some properties of the new distribution including mode, skewness, kurtosis, hazard function, and moments are studied. We propose the method of maximum likelihood to estimate the parameters and assess the finite sample size performance of the method. A generalized logistic regression model, based on the new distribution, is presented. Logistic-log-logistic regression, Weibull-extreme value regression and log-Fréchet regression are special cases of the generalized logistic regression model. The model is applied to fit failure time of a new insulation technique and the survival of a heart transplant study.

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Section: Turbocharger Datamentioning

confidence: 99%

Generalized logistic distribution and its regression model

2020

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“…The introduction of the function w ( R (⋅)) as the upper limit in the integral allows one to employ a pdf g (⋅) with support other than [0, 1]. Alzaatreh et al (2015) suggest several w (⋅) functions, e.g., w ( u )=−ln( u /(1− u )) and −ln(1− u a ) where a >0, and focus on the case when w ( u )=−ln(1− u ) and g (⋅) is the gamma pdf. The fact that H ( y )= G ( w ( R ( y ))) provides a relationship for simulations of random numbers and calculations of quantiles of the resulting distribution.…”

Section: Motivationmentioning

confidence: 99%

Methods for generating coherent distortion risk measures

Samanthi

Sepanski

2018

Ann. actuar. sci.

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This paper presents methods for generating new distortion functions utilising distribution functions and composite distribution functions. To ensure the coherency of the corresponding distortion risk measures, the concavity of the proposed distortion functions is established by restricting the parameter space of the generating distribution. Closed-form expressions for risk measures are derived for some cases. Numerical and graphical results are presented to demonstrate the effects of parameter values on the risk measures for exponential, Pareto and log-normal losses. In addition, we apply the proposed distortion functions to derive risk measures for a segregated fund guarantee.

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“…Four new generalized distributions developed namely, the Weibull-Normal{exponential}, the exponential-Normal{log-logistic}, the logistic-Normal {logistic}, and the logistic-Normal{extreme value}. [8] replaced (R) with gamma distribution to propose the family of T-gamma{Y} distributions with five subfamilies based on different quantile functions. They defined three new generalized distributions namely the Weibull-gamma{exponential}, the Weibull-gamma{log-logistic} and the Cauchy-gamma{logistic}.…”

Section: Introductionmentioning

confidence: 99%

Lomax-Gumbel {Fréchet}: A New Distribution

Mahmoud

Mandouh

Abdelatty

2019

JAMCS

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In this paper the T-R{Y} framework is used for proposing a new distribution that called The Lomax-Gumbel{Frechet} distribution. We study in details the properties of this distribution including hazard function, quantile Function, the skewness, the kurtosis, transformation, Renyi entropy, and moment generating function. Estimate of the parameters will be obtained using the MLE method. We present a simulation study and t the distribution to two real data sets.

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Family of generalized gamma distributions: Properties and applications

Cited by 19 publications

References 35 publications

Generalized logistic distribution and its regression model

Generalized logistic distribution and its regression model

Methods for generating coherent distortion risk measures

Lomax-Gumbel {Fréchet}: A New Distribution

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