The Lomax generator of distributions: Properties, minification process and regression model

Cordeiro, Gauss M.; Ortega, Edwin M. M.; Popović, Božidar V.; Pescim, Rodrigo R.

doi:10.1016/j.amc.2014.09.004

Cited by 123 publications

(98 citation statements)

References 28 publications

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“…The first real data set is a subset of the data reported by Bekker et al (2000), which corresponds to the survival times (in years) of a group of patients given chemotherapy treatment alone. 15,14,10,57,320,261,51,44,9,254,493,33,18,209,41,58,60,48,56,87,11,102,12,5,14,14,29,37,186,29,104,7,4,72,270,283,7,61,100,61,502,220,120,141,22,603,35,98,54,100,11,181,65,49,12,239,…”

Section: Applicationsmentioning

confidence: 99%

The Gumbel-Lomax Distribution: Properties and Applications

Tahir¹,

Hussain²,

Cordeiro³

et al. 2016

JSTA

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We introduce a new four-parameter model called the Gumbel-Lomax distribution arising from the Gumbel-X generator recently proposed by Al-Aqtash (2013). Its density function can be right-skewed and reversed-J shaped, and can have decreasing and upside-down bathtub shaped hazard rate. Various structural properties of the new distribution are obtained including explicit expressions for the quantile function, ordinary and incomplete moments, Lorenz and Bonferroni curves, mean residual lifetime, mean waiting time, probability weighted moments, generating function and Shannon entropy. We also provide the density function for the order statistics. Some characterizations of the new distribution based on the conditional expectations of certain functions of the random variable are also proposed. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The flexibility of the new model is illustrated by means of two real lifetime data sets.

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Section: Applicationsmentioning

confidence: 99%

The Gumbel-Lomax Distribution: Properties and Applications

Tahir¹,

Hussain²,

Cordeiro³

et al. 2016

JSTA

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“…Many generalized distribution functions are constructed in a similar manner, for example the exponentiated gamma, exponentiated Fréchet and exponentiated Gumbel distributions [23], although the way they defined the cdfs of the last two distributions is slightly different. Several other classes can be mentioned such as the Marshall-Olkin-G (MO-G) family by Marshall and Olkin [22], beta generalized-G (BG-G) family by Eugene et al [14], Kumaraswamy-G (Kw-G) family by Cordeiro and de Castro [9] and exponentiated generalized-G (EG-G) family by Cordeiro et al [8], the Lomax generator of distributions by Cordeiro et al [12], beta odd log-logistic generalized (BOLL-G) by Cordeiro et al [11], beta Marshall-Olkin (BMO-G) by Alizadeh et al [4], Kumaraswamy odd log-logistic (KwOLL-G) by Alizadeh et al [6], Kumaraswamy Marshall-Olkin (KwMO-G) by Alizadeh et al [5], generalized transmuted-G (GT-G) by Nofal et al [24], transmuted exponentiated generalized-G (TExG-G) by Yousof et al [26], Kumaraswamy transmuted-G by Afify et al [2] and transmuted geometric-G by Afify et al [1].…”

Section: Introductionmentioning

confidence: 99%

The Burr X Generator of Distributions for Lifetime Data

Yousof¹,

Afify²,

Hamedani³

et al. 2017

JSTA

108

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“…This induction of parameter(s) has been proved useful in exploring tail properties and also for improving the goodness-of-fit of the family under study. The well-known generators are the following: beta-G by Eugene et al [18], Kumaraswamy-G (Kw-G) by Cordeiro and de Castro [12], McDonald-G (Mc-G) by Alexander et al [1], gamma-G type 1 by Zografos and Balakrishanan [29] and Amini et al [7], gamma-G type 2 by Ristić and Balakrishanan [26] and Amini et al [7], odd exponentiated generalized (odd exp-G) by Cordeiro et al [14], transformed-transformer (T-X) (Weibull-X and gamma-X) by Alzaatreh et al [4], exponentiated T-X by Alzaghal et al [6], odd Weibull-G by Bourguignon et al [8], exponentiated half-logistic by Cordeiro et al [11], T-X{Y}-quantile based approach by Aljarrah et al [3], T-R{Y} by Alzaatreh et al [5], Lomax-G by Cordeiro et al [15], logistic-X by Tahir et al [28] and Kumaraswamy odd log-logistic-G by Alizadeh et al [2].…”

Section: Introductionmentioning

confidence: 99%

A New Weibull-G Family of Distributions

Tahir¹,

Zubair²,

Mansoor³

et al. 2015

HJMS

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Statistical analysis of lifetime data is an important topic in reliability engineering, biomedical and social sciences and others. We introduce a new generator based on the Weibull random variable called the new Weibull-G family. We study some of its mathematical properties. Its density function can be symmetrical, left-skewed, right-skewed, bathtub and reversed-J shaped, and has increasing, decreasing, bathtub, upside-down bathtub, J, reversed-J and S shaped hazard rates. Some special models are presented. We obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Rényi entropy, order statistics and reliability. Three useful characterizations based on truncated moments are also proposed for the new family. The method of maximum likelihood is used to estimate the model parameters. We illustrate the importance of the family by means of two applications to real data sets.

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The Lomax generator of distributions: Properties, minification process and regression model

Cited by 123 publications

References 28 publications

The Gumbel-Lomax Distribution: Properties and Applications

The Gumbel-Lomax Distribution: Properties and Applications

The Burr X Generator of Distributions for Lifetime Data

A New Weibull-G Family of Distributions

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