Inference under progressively type II right censored sampling for certain lifetime distributions

In this paper, estimation of the parameters of a certain family of two-parameter lifetime distributions based on progressively Type II right censored samples (including ordinary Type II right censoring) is studied. This family, of reverse hazard distributions, includes the Weibull, Gompertz and Lomax distributions. A new type of parameter estimation, named inverse estimation, is introduced for both parameters. Exact confidence intervals for one of the parameters and generalized confidence intervals for the other are explored; inference for the first parameter can be accomplished by our methodology independently of the unknown value of the other parameter in this family of distributions. Derivation of the estimation method uses properties of order statistics. A simulation study in the particular context of the Weibull distribution illustrates the accuracy of these confidence intervals and compares inverse estimators favorably with maximum likelihood estimators. A numerical example is used to illustrate the proposed procedures

Statistical Inference for the Transformed Rayleigh Lomax Distribution with Progressive Type-II Right Censorship

In this paper, we study the transformed Rayleigh Lomax (Trans-RL) distribution which belongs to a certain family of two parameters lifetime distributions given by Wang et al (2010). Confidence intervals and inverse estimators of the Trans-RL parameters are derived in terms of order statistics. A simulation study is conducted to report the coverage probabilities, the average biases and the average relative mean square errors for the maximum likelihood, L-moments and inverse estimators. We compare the performance of these methods under different schemes of progressively Type-II right censoring. Finally, an illustrative example is provided to demonstrate the proposed methods

Statistical Inference for the Transformed Rayleigh Lomax Distribution with Progressive Type-II Right Censorship

In this paper, we study the transformed Rayleigh Lomax (Trans-RL) distribution which belongs to a certain family of two parameters lifetime distributions given by Wang et al (2010). Confidence intervals and inverse estimators of the Trans-RL parameters are derived in terms of order statistics. A simulation study is conducted to report the coverage probabilities, the average biases and the average relative mean square errors for the maximum likelihood, L-moments and inverse estimators. We compare the performance of these methods under different schemes of progressively Type-II right censoring. Finally, an illustrative example is provided to demonstrate the proposed methods

Inference for exponential parameter under progressive Type-II censoring from imprecise lifetime

Progressively Type-II censored sampling is an important method ofobtaining data in lifetime studies. Statistical analysis oflifetime distributions under this censoring scheme is based onprecise lifetime data. However, in realsituations all observations and measurements of progressive Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. In this paper, we consider the estimation of exponential meanparameter under progressive Type-II censoring scheme, when thelifetime observations are fuzzy and are assumed to be related tounderlying crisp realization of a random sample. We propose a newmethod to determine the maximum likelihood estimate (MLE) of theunknown mean parameter. In addition, a new numerical method forparameter estimation based on fuzzy data is provided. Using the parametric bootstrapmethod, we then discuss the construction of confidence intervalsfor the mean parameter. Monte Carlo simulations are performed toinvestigate the performance of all the different proposedmethods. Finally, an illustrative example is also included

Inference About The Generalized Exponential Quantiles Based On Progressively Type-Ii Censored Data

In this study, we are interested in investigating the performance of likelihood inference procedures for the ℎ quantile of the Generalized Exponential distribution based on progressively censored data. The maximum likelihood estimator and three types of classical confidence intervals have been considered, namely asymptotic, percentile, and bootstrap-t confidence intervals. We considered Bayesian inference too. The Bayes estimator based on the squared error loss function and two types of Bayesian intervals were considered, namely the equal tailed interval and the highest posterior density interval. We conducted simulation studies to investigate and compare the point estimators in terms of their biases and mean squared errors. We compared the various types of intervals using their coverage probability and expected lengths. The simulations and comparisons were made under various types of censoring schemes and sample sizes. We presented two examples for data analysis, one of them is based on simulated data set and the other one based on a real lifetime data. Finally, we compared the classical inference and the Bayesian inference procedures. We concluded that Bias and MSE for classical statistics estimators show bitter results than the Bayesian estimators. Also, Bayesian intervals which attain the nominal error rate have the best average widths. We presented our conclusions and discussed ideas for possible future research

Some advances in life testing and reliability

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Inference for the Rayleigh Distribution Based on Progressive Type-II Fuzzy Censored Data

Classical statistical analysis of the Rayleigh distribution deals with precise information. However, in real world situations, experimental performance results cannot always be recorded or measured precisely, but each observable event may only be identified with a fuzzy subset of the sample space. Therefore, the conventional procedures used for estimating the Rayleigh distribution parameter will need to be adapted to the new situation. This article discusses different estimation methods for the parameters of the Rayleigh distribution on the basis of a progressively type-II censoring scheme when the available observations are described by means of fuzzy information. They include the maximum likelihood estimation, highest posterior density estimation and method of moments. The estimation procedures are discussed in detail and compared via Monte Carlo simulations in terms of their average biases and mean squared errors. Finally, one real data set is analyzed for illustrative purposes