Statistical analysis of Gompertz distribution based on progressively type-II censored competing risk model with binomial removals

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimators is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods

Statistical analysis of Gompertz distribution based on progressively type-II censored competing risk model with binomial removals

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimators is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods

Statistical analysis of progressively first-failure-censored data via beta-binomial removals

Progressive first-failure censoring has been widely-used in practice when the experimenter desires to remove some groups of test units before the first-failure is observed in all groups. Practically, some test groups may haphazardly quit the experiment at each progressive stage, which cannot be determined in advance. As a result, in this article, we propose a progressively first-failure censored sampling with random removals, which allows the removal of the surviving group(s) during the execution of the life test with uncertain probability, called the beta-binomial probability law. Generalized extreme value lifetime model has been widely-used to analyze a variety of extreme value data, including flood flows, wind speeds, radioactive emissions, and others. So, when the sample observations are gathered using the suggested censoring plan, the Bayes and maximum likelihood approaches are used to estimate the generalized extreme value distribution parameters. Furthermore, Bayes estimates are produced under balanced symmetric and asymmetric loss functions. A hybrid Gibbs within the Metropolis-Hastings method is suggested to gather samples from the joint posterior distribution. The highest posterior density intervals are also provided. To further understand how the suggested inferential approaches actually work in the long run, extensive Monte Carlo simulation experiments are carried out. Two applications of real-world datasets from clinical trials are examined to show the applicability and feasibility of the suggested methodology. The numerical results showed that the proposed sampling mechanism is more flexible to operate a classical (or Bayesian) inferential approach to estimate any lifetime parameter

A Comparison between Maximum Likelihood and Bayesian Estimation Methods for a Shape Parameter of the Weibull-Exponential Distribution

We considered the Bayesian analysis of a shape parameter of the Weibull-Exponential distribution in this paper. We assumed a class of non-informative priors in deriving the corresponding posterior distributions. In particular, the Bayes estimators and associated risks were calculated under three different loss functions. The performance of the Bayes estimators was evaluated and compared to the method of maximum likelihood under a comprehensive simulation study. It was discovered that for the said parameters to be estimated, the quadratic loss function under both uniform and Jeffrey’s priors should be used for decreasing parameter values while the use of precautionary loss function can be preferred for increasing parameter values irrespective of the variations in sample size

Optimal Progressive Group-Censoring Plans for Chen Distribution under Cost Constraint

[[abstract]]In this paper, the optimal design of a progressively group-censored life test with the restriction of experimental budget is developed for the Chen distribution is considered. The maximum likelihood estimates, approximate confidence intervals for the parameters based on progressively group-censored sample are obtained. Wu et al.’s (2008a) approach is used to determine the number of test units, the number of inspections and the length of inspection interval of a life test under a pre-determined budget of experiment such that the determinant of the asymptotic variances-covariance matrix of estimators of parameters is minimum. A numerical example is presented and the sensitivity analysis is also studied.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

Competing risk models in reliability systems, an Exponential distribution model with Gamma prior distribution, a Bayesian analysis approach

This paper is a second paper on the use of Exponential distribution in competing risk problems. The difference is this model is developed using Gamma distribution as its prior distribution. For the cases where the failure data together with their causes of failure are simply quantitatively inadequate, time consuming and expensive to perform the life tests, especially in engineering areas, Bayesian analysis approach is used. This model is limited for independent causes of failure. In this paper our effort is to introduce the basic notions that constitute an exponential competing risks model in reliability using Bayesian analysis approach and presenting their analytic methods. Once the model has been develop through the system likelihood function and individual posterior distributions then the parameter of estimates are derived. The results are the estimations of the failure rate of individual risk, the MTTF of individual and system risks, and the reliability estimations of the individual and of the system of the model

Planning life tests for Burr XII distributed products under progressive group-censoring with cost considerations

[[abstract]]In this paper, a progressive type I group-censoring life test for Burr XII distribution is considered. We use the maximum likelihood method to obtain the point estimators of the Burr XII parameters. The approximate confidence intervals for the parameters of Burr XII distribution are also obtained. We use modified algorithm proposed by Kus et al. [20] to decide the number of test units, number of inspections, and length of inspection interval under a restricted budget of experiment such that the determinant of the asymptotic variances-covariance of estimators of parameters is minimum. A numerical example is presented to illustrate the proposed approach. The sensitivity analysis is also investigated.[[journaltype]]國外[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]電子版[[countrycodes]]TU

Statistical inference for the Nadarajah-Haghighi distribution based on ranked set sampling with applications

In this article, the maximum likelihood and Bayes inference methods are discussed for determining the two unknown parameters and specific lifetime parameters of the Nadarajah-Haghighi distribution, such as the survival and hazard rate functions, with the inclusion of ranked set sampling and simple random sampling. The estimated confidence intervals for the two parameters and any function of them are developed based on the Fisher-information matrix. Metropolis-Hastings algorithm and Lindley-approximation are used for generating the Bayes estimates and related highest posterior density credible ranges for the unknown parameters and reliability parameters under the presumption of conjugate gamma priors. A Monte-Carlo simulation study and a real-life data set have been used to assess the efficacy of the proposed methods

Random Number Generators

The quasi-negative-binomial distribution was applied to queuing theory for determining the distribution of total number of customers served before the queue vanishes under certain assumptions. Some structural properties (probability generating function, convolution, mode and recurrence relation) for the moments of quasi-negative-binomial distribution are discussed. The distribution’s characterization and its relation with other distributions were investigated. A computer program was developed using R to obtain ML estimates and the distribution was fitted to some observed sets of data to test its goodness of fit