Exponentiated Weibull family for analyzing bathtub failure-rate data

Mudholkar, Govind S.; Srivastava, Divesh

doi:10.1109/24.229504

Cited by 1,018 publications

(588 citation statements)

References 7 publications

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“…The properties of these distributions have been studied by many authors in recent years. See, for example, Mudholkar et al (1995) and Mudholkar and Srivastava (1993) for exponentiated Weibull, Gupta et al (1998) for exponentiated Pareto, Nadarajah (2005) for exponentiated Gumbel, Nadarajah and Gupta (2007) for exponentiated gamma, and Lemonte (2012) for exponentiated Kumaraswamy (Kw), among others. Cordeiro and Lemonte (2015) proved, using (10) twice in equation (4), that the EG cdf can be expressed as…”

Section: Useful Representationsmentioning

confidence: 99%

The Extended Log-Logistic Distribution: Properties and Application

Lima

Cordeiro

2017

An. Acad. Bras. Ciênc.

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We propose a new four-parameter lifetime model, called the extended log-logistic distribution, to generalize the two-parameter log-logistic model. The new model is quite flexible to analyze positive data. We provide some mathematical properties including explicit expressions for the ordinary and incomplete moments, probability weighted moments, mean deviations, quantile function and entropy measure. The estimation of the model parameters is performed by maximum likelihood using the BFGS algorithm. The flexibility of the new model is illustrated by means of an application to a real data set. We hope that the new distribution will serve as an alternative model to other useful distributions for modeling positive real data in many areas.

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Section: Useful Representationsmentioning

confidence: 99%

The Extended Log-Logistic Distribution: Properties and Application

Lima

Cordeiro

2017

An. Acad. Bras. Ciênc.

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“…The properties of Exp-G distributions have been studied by many authors in recent years, see Mudholkar and Srivastava (1993) and Mudholkar, Srivastava, and Freimer (1995) for exponentiated Weibull, Gupta, Gupta, and Gupta (1998) for exponentiated Pareto, Gupta and Kundu (1999) for exponentiated exponential, Nadarajah (2005) for exponentiated Gumbel, Shirke and Kakade (2006) for exponentiated log-normal and Nadarajah and Gupta (2007) for exponentiated gamma distributions.…”

Section: Useful Expansionsmentioning

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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“…These include modified Weibull distribution and its extension models [1][2][3][4][5], exponentiated Weibull family [6][7][8], mixture models [9][10], competing risk models, multiplicative models and sectional models [11][12][13][14]. These models can be utilized to analyze a given data set whose fitting plot on WPP is concave, convex, S-shaped or further other shapes.…”

Section: Introductionmentioning

confidence: 99%

Choosing an optimal model for failure data analysis by graphical approach

Zhang

Dwight

2013

Reliability Engineering & System Safety

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Many models involving combination of multiple Weibull distributions, modification of Weibull distribution or extension of its modified ones, etc. have been developed to model a given set of failure data. The application of these models to modeling a given data set can be based on plotting the data on Weibull probability paper (WPP). Of them, two or more models are appropriate to model one typical shape of the fitting plot, whereas a specific model may be fit for analyzing different shapes of the plots. Hence, a problem arises, that is how to choose an optimal model for a given data set and how to model the data. The motivation of this paper is to address this issue. This paper summarizes the characteristics of Weibull-related models with more than three parameters including sectional models involving two or three Weibull distributions, competing risk model and mixed Weibull model. The models as discussed in this present paper are appropriate to model the data of which the shapes of plots on WPP can be concave, convex, S-shaped or inversely S-shaped. Then, the method for model selection is proposed, which is based on the shapes of the fitting plots. The main procedure for parameter estimation of the models is described accordingly. In addition, the range of data plots on WPP is clearly highlighted from the practical point of view. To note this is important as mathematical analysis of a model with neglecting the applicable range of the model plot will incur discrepancy or big errors in model selection and parameter estimates. © 2013 Elsevier Ltd. All rights reserved. The application of these models to modeling a given data set can be based on plotting the data on Weibull probability paper (WPP). Of them, two or more models are appropriate to model one typical shape of the fitting plot, whereas a specific model may be fit for analyzing different shapes of the plots. Hence, a problem arises, that is how to choose an optimal model for a given data set and how to model the data. The motivation of this paper is to address this issue. This paper summarizes the characteristics of Weibull-related models with more than three parameters including sectional models involving two or three Weibull distributions, competing risk model and mixed Weibull model. The models as discussed in this present paper are appropriate to model the data of which the shapes of plots on WPP can be concave, convex, S-shaped or inversely S-shaped. Then, the method for model selection is proposed, which is based on the shapes of the fitting plots. The main procedure for parameter estimation of the models is described accordingly. In addition, the range of data plots on WPP is clearly highlighted from the practical point of view. To note this is important as mathematical analysis of a model with neglecting the applicable range of the model plot will incur discrepancy or big errors in model selection and parameter estimates.Keywords: Weibull models, Failure data analysis, Model selection, Parameter estimation, Weibull probability paper NOTATION...

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Exponentiated Weibull family for analyzing bathtub failure-rate data

Cited by 1,018 publications

References 7 publications

The Extended Log-Logistic Distribution: Properties and Application

The Extended Log-Logistic Distribution: Properties and Application

The Odd Lindley-G Family of Distributions

Choosing an optimal model for failure data analysis by graphical approach

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