Finite Mixture Distributions

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment The mixture model of two generalized inverse Weibull distributions is investigated The identifiability property of the mixture model is demonstrated For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data In addition, we develop some diagnostic tools for sensitivity analysis Two applications of real data are given to illustrate the potentiality of the proposed regression model

The generalized inverse Weibull distribution

Modifications of the Weibull distribution: A review

A discrete inverse Weibull distribution and estimation of its parameters

In the modern scenario, reliability has becomes the most challenging and demanding theory. The theory and the methods of reliability analysis have been developed significantly during the last 40 years and have also been acknowledged in a number of publications. So, a reliability engineer is aware about the importance of each reliability measure of the system and its fields. In this research work, a survey of reliability approaches in various fields of engineering and physical sciences is carried out. In this survey, the author tried to provide the major areas i.e. past, current and future trends of reliability methods and applications for the readers.

On system reliability approaches: a brief survey

Mixture of two inverse Weibull distributions: Properties and estimation

The Truncated Cauchy Power Weibull-G class is presented as a new family of distributions. Unique models for this family are presented in this paper. The statistical aspects of the family are explored, including the expansion of the density function, moments, incomplete moments (IMOs), residual life and reversed residual life functions, and entropy. The maximum likelihood (ML) and Bayesian estimations are developed based on the Type-II censored sample. The properties of Bayes estimators of the parameters are studied under different loss functions (squared error loss function and LINEX loss function). To create Markov-chain Monte Carlo samples from the posterior density, the Metropolis–Hasting technique was used with posterior density. Using non-informative and informative priors, a full simulation technique was carried out. The maximum likelihood estimator was compared to the Bayesian estimators using Monte Carlo simulation. To compare the performances of the suggested estimators, a simulation study was carried out. Real-world data sets, such as strength measured in GPA for single carbon fibers and impregnated 1000-carbon fiber tows, maximum stress per cycle at 31,000 psi, and COVID-19 data were used to demonstrate the relevance and flexibility of the suggested method. The suggested models are then compared to comparable models such as the Marshall–Olkin alpha power exponential, the extended odd Weibull exponential, the Weibull–Rayleigh, the Weibull–Lomax, and the exponential Lomax distributions.

/pdf/truncated-cauchy-power-weibull-g-class-of-distributions-358p6tbv.pdf

Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data

The main goal of this paper is to develop the approximate Bayes estimation of the five-dimensional vector of the parameters and reliability function of a mixture of two inverse Weibull distributions (MTIWD) under Type-2 censoring. Usually, the posterior distribution is complicated under the scheme of Type-2 censoring and the integrals that are involved cannot be obtained in a simple explicit form. In this study, we use Lindley's [Approximate Bayesian method, Trabajos Estadist. 31 (1980), pp. 223–237] approximate form of Bayes estimation in the case of an MTIWD under Type-2 censoring. Later, we calculate the estimated risks (ERs) of the Bayes estimates and compare them with the corresponding ERs of the maximum-likelihood estimates through Monte Carlo simulation. Finally, we analyse a real data set using the findings.

Approximate Bayes estimation of the parameters and reliability function of a mixture of two inverse Weibull distributions under Type-2 censoring

The classification of a random variable based on a mixture can be meaningfully discussed only if the class of all finite mixtures is identifiable. In this paper, we find the maximum-likelihood estimates of the parameters of the mixture of two inverse Weibull distributions by using classified and unclassified observations. Next, we estimate the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification as well as the percentage bias. In addition, we investigate the performance of all results through a series of simulation experiments by means of relative efficiencies. Finally, we analyse some simulated and real data sets through the findings of the paper.

/pdf/estimation-of-a-discriminant-function-from-a-mixture-of-two-5er77ghjai.pdf

Estimation of a discriminant function from a mixture of two inverse Weibull distributions

In this paper, we use the likelihood ratio test (LRT) for testing the number of components in a mixture of two inverse Weibull distributions (MTIWD). First, we formulate the null distribution of the likelihood ratio statistic. Next, we calculate the percentage points of the test statistic under two different stopping criteria. In addition, we compute the power of the proposed test under these two stopping criteria and show that global maximization of the likelihood is not necessary to obtain a good power of the LRT. Finally, we discuss two applications to illustrate whether a set of data arises from a single or a MTIWD.

A. S. Al-Moisheer

Papers

Mixture of two inverse Weibull distributions: Properties and estimation

Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data

Approximate Bayes estimation of the parameters and reliability function of a mixture of two inverse Weibull distributions under Type-2 censoring

Estimation of a discriminant function from a mixture of two inverse Weibull distributions

Testing the number of components of the mixture of two inverse Weibull distributions