The Generalized Inverse Generalized Weibull Distribution and Its Properties

Jain, Kanchan; Singla, Neetu; Sharma, Suresh

doi:10.1155/2014/736101

Cited by 9 publications

(3 citation statements)

References 15 publications

(19 reference statements)

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“…Table (1) shows some numerical values for the skewness and kurtosis of the two-component mixture at various combinations of the model parameters. We used the skewness-kurtosis plot to validate the numerical values.…”

Section: Properties Of the Fmwemmentioning

confidence: 99%

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Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

Mohamed¹,

Ismail²,

Ismail³

2022

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Finite mixture models have been used in many fields of statistical analysis such as pattern recognition, clustering and survival analysis, and have been extensively applied in different scientific areas such as marketing, economics, medicine, genetics and social sciences. Introducing mixtures of new generalized lifetime distributions that exhibit important hazard shapes is a major field of research aiming at fitting and analyzing a wider variety of data sets. The main objective of this article is to present a full mathematical study of the properties of the new finite mixture of the three-parameter Weibull extension model, considered as a generalization of the standard Weibull distribution. The new proposed mixture model exhibits a bathtub-shaped hazard rate among other important shapes in reliability applications. We analytically prove the identifiability of the new mixture and investigate its mathematical properties and hazard rate function. Maximum likelihood estimation of the model parameters is considered. The Kolmogrov-Smirnov test statistic is used to fit two famous data sets from mechanical engineering to the proposed model, the Aarset data and the Meeker and Escobar datasets. Results show that the two-component version of the proposed mixture is a superior fit compared to various lifetime distributions, either one-component or two-component lifetime distributions. The new proposed mixture is a significant statistical tool to study lifetime data sets in numerous fields of study.

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Section: Properties Of the Fmwemmentioning

confidence: 99%

“…A number of distributions were developed as generalizations or modifications of the Weibull distribution. Reference [1] introduced the Inverse generalized Weibull and generalized Inverse generalized Weibull (GIGW) distributions. They investigated the mixture model of two-component GIGW distributions.…”

Section: Introductionmentioning

confidence: 99%

Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

Mohamed¹,

Ismail²,

Ismail³

2022

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“…The three parameter Gompertz-Lindley distribution (GLD) of Koleoso et al (2019) The extended log-inverse Weibull distribution (ELIWD) of Kumar and Nair (2018c) The three parameter Lindley distribution (LD) of Shanker et al (2017) The exponentiated power Lindley distribution (EPLD) of Ashour and Eltehiwy (2015) The Kumaraswamy modified inverse Weibull distribution (KMIWD) of Aryal and Elbatal (2015) The inverse generalized Weibull distribution (IGWD) of Jain et al (2014) The generalized inverse generalized Weibull distribution (GIGWD) of Jain et al (2014) The generalized inverse Weibull distribution (GIWD) of de Gusmao et al (2011) The exponentiated generalised inverse Weibull distribution (EGIWD) of Elbatal (2011) The log-generalized inverse Weibull distribution (LGIWD) of de Gusmao et al (2011) All the above distributions are fitted to Data sets 1, 2 using the likelihood function ( 54) and ( 56) for complete and censored data sets respectively. In both these cases it can be seen that the ExLIWD provides the best fit to the data sets while the GIGWD is seen to be the distribution providing the next best fit.…”

Section: Applicationsmentioning

confidence: 99%

A generalization to the log-inverse Weibull distribution and its applications in cancer research

Kumar

Nair

2021

J Stat Distrib App

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In this paper we consider a generalization of a log-transformed version of the inverse Weibull distribution. Several theoretical properties of the distribution are studied in detail including expressions for its probability density function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, percentile measures, entropy measures, median, mode etc. Certain structural properties of the distribution along with expressions for reliability measures as well as the distribution and moments of order statistics are obtained. Also we discuss the maximum likelihood estimation of the parameters of the proposed distribution and illustrate the usefulness of the model through real life examples. In addition, the asymptotic behaviour of the maximum likelihood estimators are examined with the help of simulated data sets.

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Generalized Gompertz-generalized inverse Weibull distribution

Abid¹,

Jani²

2022

1st Samarra International Conference for Pure and Applied Sciences (Sicps2021): Sicps2021

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The Generalized Inverse Generalized Weibull Distribution and Its Properties

Cited by 9 publications

References 15 publications

Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

A generalization to the log-inverse Weibull distribution and its applications in cancer research

Generalized Gompertz-generalized inverse Weibull distribution

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