A new generalized Weibull distribution generated by gamma random variables

Castellares, Fredy; Lemonte, Artur J.

doi:10.1016/j.joems.2014.03.009

Cited by 21 publications

(7 citation statements)

References 28 publications

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“…The properties such as existence, uniqueness of roots for log and log q likelihood functions of the censoring designs which can be regarded as objective function [41] will be studied. install.packages("CDFt") library("CDFt") val_CDFbiWeiq=CDFbiWei(sort(x),mleBiWeiabq [1],mleBiWeiabq [2],mleBiWeiabq [3]) fun.ecdf=ecdf(x);my.ecdf <-fun.ecdf(sort(x)); ks.test(my.ecdf, val_CDFbiWeiq,alternative = c("two.sided", "less", "greater"), exact = NULL, tol=1e-8,simulate.p.value=FALSE,B=2000) resq = CramerVonMisesTwoSamples(my.ecdf,val_CDFbiWeiq); pvalueCVMq = 1/6*exp(-resq);…”

Section: Discussionmentioning

confidence: 99%

“…In other words, a data set can be a combination of different parametric models or different values of same parametric model f (x; θ) to represent bimodality [5,25,26]. The light tailed property, tractability of analytical expression, bimodality kernel 1 + (1 − δx) 2 used to derive only one mode property occurred due to the polynomial degree 2 [8], and also for confining yourself for modelling data set having two modes at the different degree high of peakedness can require to apply bimodality generator for Weibull distribution.…”

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confidence: 99%

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A Bimodal Weibull Distribution: Properties and Inference

Vila¹,

Çankaya²

2020

Preprint

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Modeling is a challenging topic and using parametric models is an important stage to reach flexible function for modeling. Weibull distribution has two parameters which are shape α and scale β. In this study, bimodality parameter is added and so bimodal Weibull distribution is proposed by using a quadratic transformation technique used to generate bimodal functions produced due to using the quadratic expression. The analytical simplicity of Weibull and quadratic form give an advantage to derive a bimodal Weibull via constructing normalizing constant. The characteristics and properties of the proposed distribution are examined to show its usability in modeling. After examination as first stage in modeling issue, it is appropriate to use bimodal Weibull for modeling data sets. Two estimation methods which are maximum log q likelihood and its special form including objective functions log q (f ) and log(f ) are used to estimate the parameters of shape, scale and bimodality parameters of the function. The second stage in modeling is overcome by using heuristic algorithm for optimization of function according to parameters due to fact that converging to global point of objective function is performed by heuristic algorithm based on the stochastic optimization.Real data sets are provided to show the modeling competence of the proposed distribution.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

A Bimodal Weibull Distribution: Properties and Inference

Vila¹,

Çankaya²

2020

Preprint

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“…Gamma G distributions have been used to model: breaking stress of carbon fibers (Alzaatreh et al 2014;Cordeiro et al 2014a); flood levels for the Susquehanna river at Harrisburg, PA (Alzaatreh and Knight 2013); gene expression levels on human cancer cells ; number of million of revolutions before failure of ball bearings in a life testing experiment (Pararai et al 2014); number of successive failures for the air conditioning system of each member in a fleet of Boeing 720 jet airplanes (Oluyede et al 2014); remission times of a random sample of bladder cancer patients (Cordeiro et al 2015;Oluyede et al 2014;Castellares and Lemonte 2015); salaries of professional baseball players (Oluyede et al 2014); strengths of glass fibers (Alzaatreh et al 2014); survival times of breast cancer patients (Ramos et al 2013); survival times of cutaneous melanoma (a type of malignant cancer) patients (Cordeiro et al 2014a); survival times of guinea pigs injected with different doses of tubercle bacilli (Pararai et al 2014); tensile strength for single-carbon fibers (Alzaatreh and Knight 2013); the cDNA microarray data of the NC160 cancer cell lines ; waiting times between consecutive eruptions of the Kiama Blowhole (Silva et al 2013).…”

Section: Families Of Distributions and R Codementioning

confidence: 99%

Newdistns: AnRPackage for New Families of Distributions

Nadarajah

Rocha²

2016

J. Stat. Soft.

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The contributed R package Newdistns written by the authors is introduced. This package computes the probability density function, cumulative distribution function, quantile function, random numbers and some measures of inference for nineteen families of distributions. Each family is flexible enough to encompass a large number of structures. The use of the package is illustrated using a real data set. Also robustness of random number generation is checked by simulation.

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“…Special Models). Numerous authors have linked to listed models considering special cases of Gamma generalized, exponentiated distribution classes, among others we refer to Gamma-exponentiated Weibull [9,10], exponentiated Weibull, exponentiated Pareto, exponentiated Gamma [11], Kumaraswamy generalized Gamma and Gumbel [12,13] distributions with exhaustive references lists and links to further sub-models and special cases, consult e.g., ( [13], pp. 415-416); also see the recent article [14] where an extension is obtained for the generalized integro-exponential function by which the moment expression of the above listed distribution classes can be expressed in a closed or more compact form.…”

Section: Introductionmentioning

confidence: 99%