A Family of Lifetime Distributions

Pappas, Vasileios; Adamidis, Konstantinos; Loukas, S.

doi:10.1155/2012/760687

Cited by 28 publications

(21 citation statements)

References 20 publications

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“…So, several classes by adding shape parameters to generate new models have been explored in the statistical literature. We propose a new generalization of the three-parameter extended Weibull distribution pioneered by Pappas et al (2012) by using the generator by Marshall and Olkin (1997). The new model is called the (P-A-L) extended Weibull, where (P-A-L) denote the first letters of the scientists Pappas, Adamidis and Loukas.…”

Section: Introductionmentioning

confidence: 99%

“…However, this distribution does not provide a reasonable parametric fit for some practical applications where the underlying hazard rates may be bathtub or unimodal shapes. [13] introduced a new generalization of any distribution, which is derived by using the generator * Departament of Statistics, King Abdulaziz University, Saudi Arabia.…”

Section: Introductionmentioning

confidence: 99%

“…[13] proposed the (P-A-L) extended family with the additional parameter p > 1, where the survival function F (t), cdf F (t) and pdf f (t) are given by (for t > 0) (1.3) F (t) = log 1 − (1 − p) G(t) log(p) ,…”

Section: Introductionmentioning

confidence: 99%

“…Further, [13] studied the (P-A-L) extended modified Weibull distribution. In this paper, we take the EW distribution given by (1.1) as the baseline model to define a new four-parameter (P-A-L) extended Weibull, say the (P-A-L)EW distribution.…”

Section: Introductionmentioning

confidence: 99%

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The (P-A-L) Extended Weibull Distribution: A New Generalization of the Weibull Distribution

Alzahrani

Marinho²,

Fattah³

et al. 2015

HJMS

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Recently, some attempts have been made to construct new families of models to extend well-known distributions and at the same time provide great flexibility in modeling data in practice. So, several classes by adding shape parameters to generate new models have been explored in the statistical literature. We propose a new generalization of the three-parameter extended Weibull distribution pioneered by Pappas et al. (2012) by using the generator by Marshall and Olkin (1997). The new model is called the (P-A-L) extended Weibull, where (P-A-L) denote the first letters of the scientists Pappas, Adamidis and Loukas.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The (P-A-L) Extended Weibull Distribution: A New Generalization of the Weibull Distribution

Alzahrani

Marinho²,

Fattah³

et al. 2015

HJMS

View full text Add to dashboard Cite

show abstract

“…An overview on the Weibull models can be found in [15]. In recent years, there are many research papers published on the extended Weibull and modified Weibull distributions and their applications, see for example, [5,[16][17][18][19][20][21][22]. The interest is that each of the distribution models can present a hazard function that is decreasing, increasing or bathtub shaped.…”

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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A weighted general family of distributions: Theory and practice

Bakouch

Chesneau

Enany

2020

Comp and Math Methods

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In this article, we introduce a new general family of distributions. The submodels of the general family accommodate various shapes of pdf and hazard rate, involving decreasing, increasing, bathtub and J-shapes. Hence, it can provide analysis for many practical datasets. Mathematical expressions for the family are obtained, including moments, moment generating and quantile functions, stochastic ordering, and entropy. Some submodels of the family are inserted based on the baseline distributions: Exponential, Gompertz, Lindley, and weight exponential distributions. Estimation of the model parameters is justified by the method of maximum likelihood. Capability of the family is shown by fitting three practical datasets to the mentioned submodels. K E Y W O R D Sfamily of distributions, goodness-of-fit statistics, statistical and reliability properties, weighted distributionsComp and Math Methods.

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A Family of Lifetime Distributions

Cited by 28 publications

References 20 publications

The (P-A-L) Extended Weibull Distribution: A New Generalization of the Weibull Distribution

The (P-A-L) Extended Weibull Distribution: A New Generalization of the Weibull Distribution

Choosing an optimal model for failure data analysis by graphical approach

A weighted general family of distributions: Theory and practice

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