A new method for generating families of continuous distributions

We propose a new lifetime model called the transmuted geometric-Weibull distribution. Some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Rényi and q-entropies and order statistics are derived. The maximum likelihood method is discussed to estimate the model parameters by means of Monte Carlo simulation study. A new location-scale regression model is introduced based on the proposed distribution. The new distribution is applied to two real data sets to illustrate its flexibility. Empirical results indicate that proposed distribution can be alternative model to other lifetime models available in the literature for modeling real data in many areas.

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“…The quantile function (qf ) of , where :TG-W( , , , ), is obtained by inverting (3) to obtain ( ) = −1 ( ) as…”

Section: Quantile Functionmentioning

confidence: 99%

The Transmuted Geometric-Weibull distribution: Properties, Characterizations and Regression Models

Nofal

Gebaly

Altun

et al. 2017

Pak.j.stat.oper.res.

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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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“…Consequently, recent developments focus on definition of the new families of distributions that extend well-known distributions and at the same time provide great flexibility in modelling data in practice. Some well-established generators and other recently proposed are the Marshall-Olkin generated family (MO-G) by Marshall and Olkin (1997), beta-G by Eugene, Lee, and Famoye (2002), Kumaraswamy-G (Kw-G for short) by Cordeiro and de Castro (2011), McDonald-G (Mc-G) by Alexander, Cordeiro, Ortega, and Sarabia (2012), gamma-G by Zografos and Balakrishnan (2009), transformed-transformer (T-X) by Alzaatreh, Lee, and Famoye (2013), exponentiated T-X by Alzaghal, Felix, and Carl (2013), Weibull-G by Bourguignon, Silva, and Cordeiro (2014), exponentiated half-logistic family by Cordeiro, Alizadeh, and Ortega (2014), logistic-X by Tahir, Cordeiro, Alzaatreh, Mansoor, and Zubair (2016a), a new Weibull-G by Tahir, Zubair, Mansoor, Cordeiro, Alizadeh, and Hamedani (2016b) and Kumaraswamy odd log-logistic-G by Alizadeh, Emadi, Doostparast, Cordeiro, Ortega, and Pescim (2015). The Lindley distribution was originally proposed by Lindley (1958) as a counterexample of fiducial statistics.…”

Section: Introductionmentioning

confidence: 99%

The Odd Lindley-G Family of Distributions

Gomes-Silva¹,

Percontini²,

Brito³

et al. 2017

AJS

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We propose a new generator of continuous distributions with one extra positive parameter called the odd Lindley-G family. Some special cases are presented. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Various structural properties of the new family, which hold for any baseline model, are derived including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, Rényi entropy, reliability, order statistics and their moments and k upper record values. We provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates. We discuss estimation of the model parameters by maximum likelihood and provide an application to a real data set.

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A new method for generating families of continuous distributions

Cited by 843 publications

References 33 publications

The Transmuted Geometric-Weibull distribution: Properties, Characterizations and Regression Models

The Transmuted Geometric-Weibull distribution: Properties, Characterizations and Regression Models

The Gumbel-Lomax Distribution: Properties and Applications

The Odd Lindley-G Family of Distributions

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