Mixture of two inverse Weibull distributions: Properties and estimation

Sultan, Khalaf S.; Ismail, Moshira A.; Al-Moisheer, A. S.

doi:10.1016/j.csda.2006.09.016

Cited by 101 publications

(59 citation statements)

References 11 publications

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“…The cumulative hazard rate function   ; H y  and reversed hazard rate function   ; r y  for a 3-CMPD using (5) and (6) …”

Section: Cumulative Hazard Rate and Reversed Hazard Rate Functions Fomentioning

confidence: 99%

“…Usually, reliability analysis is carried out using the classical or bayesian statistical analysis of parametric reliability models. Reliability analysis data sets are represented with a single univariate or multivariate statistical distributions such as Exponential, Rayleigh, inverse Weibull, Pareto and Burr distributions [1][2][3][4][5][6]. Recently, some other distributions have been used to model the survival data.…”

Section: Introductionmentioning

confidence: 99%

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Reliability analysis of 3-component mixture of distributions

2017

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Abstract. This article focuses on studying 3-component mixtures of Exponential, Rayleigh, Pareto and Burr Type-XII distributions in relation to reliability analysis. The main purpose of this study is to derive algebraic expressions for different functions of survival time. For these 3-component mixture distributions, the cumulative distribution function, hazard rate function, cumulative hazard rate function, reversed hazard rate function, mean residual life function and mean waiting time function are discussed. To study the behavior of different reliability functions, numerical results are presented for fixed values of parameters.

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“…The cumulative hazard rate function   ; H y  and reversed hazard rate function   ; r y  for a 3-CMPD using (5) and (6) …”

Section: Cumulative Hazard Rate and Reversed Hazard Rate Functions Fomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reliability analysis of 3-component mixture of distributions

2017

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“…Examples in this direction include finite mixtures of binomial and Poisson distributions (McLachlan and Peel [19]), Weibull distribution (Jiang and Murthy [9]), inverse Weibull distribution (Sultan et al [22]), Multivariate t-distribution (Andrews and McNicholas [1]) and Multivariate skew t-distribution (Lee and McLachlan [15]). For a general discussion on parameter estimation in finite mixture of distributions and related applications, one may refer to Everitt and Hand [5], Titterington et al [23], McLachlan and Peel [19] and Melnykov and Maitra [20].…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation in Gamma Mixture Model using Normal-based Approximation

Lakshmi¹,

Vaidyanathan²

2016

JSTA

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Gamma mixture models have wide applications in hydrology, finance and reliability. Parameter estimation in this class of models is a challenging task owing to the complexity associated with the model structure. In this paper, a novel approach is proposed to estimate the parameters of Gamma mixture models using Wilson-Hilferty normalbased approximation method. The proposed methodology uses a popular clustering algorithm for Gaussian mixtures namely, MCLUST and a confidence interval based search approach to obtain the estimates. The methodology is implemented on simulated as well as real-life datasets and its performance is compared with gammamixEM() function available in R.

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“…Jiang et al (2001) discussed the models involving two inverse Weibull distributions. Sultan et al (2007) discussed the mixture of two inverse Weibull distributions. In recent literature modified extensions of the Weibull distributions for modelling bathtub instantaneous failure rates have been proposed by many authors.…”

Section: Introductionmentioning

confidence: 99%

New generalized inverse Weibull distribution for lifetime modeling

Khan

King

2016

Communications for Statistical Applications and Methods

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This paper introduces the four parameter new generalized inverse Weibull distribution and investigates the potential usefulness of this model with application to reliability data from engineering studies. The new extended model has upside-down hazard rate function and provides an alternative to existing lifetime distributions. Various structural properties of the new distribution are derived that include explicit expressions for the moments, moment generating function, quantile function and the moments of order statistics. The estimation of model parameters are performed by the method of maximum likelihood and evaluate the performance of maximum likelihood estimation using simulation.

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Mixture of two inverse Weibull distributions: Properties and estimation

Cited by 101 publications

References 11 publications

Reliability analysis of 3-component mixture of distributions

Reliability analysis of 3-component mixture of distributions

Parameter Estimation in Gamma Mixture Model using Normal-based Approximation

New generalized inverse Weibull distribution for lifetime modeling

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