A Novel Frechet-Type Probability Distribution: Its Properties and Applications

In this article, a new lifetime model, referred to as modified Frechet–Rayleigh distribution (MFRD), is developed by accommodating an additional parameter in Rayleigh distribution on the basis of the modified Frechet method. Numerous statistical properties of the suggested model are derived and discussed. The technique of maximum likelihood (ML) estimation is adopted to get estimates of the parameters. The suggested model is very flexible and has the capability to model datasets having both monotonic and nonmonotonic failure rates. The proposed model is applied on two real datasets for checking its performance in comparison with available well-known models. The suggested model has shown outclass performance in comparison with the available versions of the Rayleigh distribution used in the literature.

Comparative Study of New and Traditional Estimators of a New Lifetime Model

In this article, we have studied the behavior of estimators of parameter of a new lifetime model, suggested by Maurya et al. (2016), obtained by using methods of moments, maximum likelihood, maximum product spacing, least squares, weighted least squares, percentile, Cramer-von-Mises, Anderson-Darling and Right-tailed Anderson-Darling. Comparison of the estimators has been done on the basis of their mean square errors, biases, absolute and maximum absolute differences between empirical and estimated distribution function and a newly proposed criterion. We have also obtained the asymptomatic confidence interval and associated coverage probability for the parameter.

On inference and design under progressive type-I interval censoring scheme for inverse Gaussian lifetime model

PurposeThis article considers Inverse Gaussian distribution as the basic lifetime model for the test units. The unknown model parameters are estimated using the method of moments, the method of maximum likelihood and Bayesian methods. As part of maximum likelihood analysis, this article employs an expectation-maximization algorithm to simplify numerical computation. Subsequently, Bayesian estimates are obtained using the Metropolis–Hastings algorithm. This article then presents the design of optimal censoring schemes using a design criterion that deals with the precision of a particular system lifetime quantile. The optimal censoring schemes are obtained after taking into account budget constraints.Design/methodology/approachThis article first presents classical and Bayesian statistical inference for Progressive Type-I Interval censored data. Subsequently, this article considers the design of optimal Progressive Type-I Interval censoring schemes after incorporating budget constraints.FindingsA real dataset is analyzed to demonstrate the methods developed in this article. The adequacy of the lifetime model is ensured using a simulation-based goodness-of-fit test. Furthermore, the performance of various estimators is studied using a detailed simulation experiment. It is observed that the maximum likelihood estimator relatively outperforms the method of moment estimator. Furthermore, the posterior median fares better among Bayesian estimators even in the absence of any subjective information. Furthermore, it is observed that the budget constraints have real implications on the optimal design of censoring schemes.Originality/valueThe proposed methodology may be used for analyzing any Progressive Type-I Interval Censored data for any lifetime model. The methodology adopted to obtain the optimal censoring schemes may be particularly useful for reliability engineers in real-life applications.

Statistical Properties of a New Bathtub Shaped Failure Rate Model With Applications in Survival and Failure Rate Data

In this study, we proposed a flexible lifetime model identified as the modified exponentiated Kumaraswamy (MEK) distribution. Some distributional and reliability properties were derived and discussed, including explicit expressions for the moments, quantile function, and order statistics. We discussed all the possible shapes of the density and the failure rate functions. We utilized the method of maximum likelihood to estimate the unknown parameters of the MEK distribution and executed a simulation study to assess the asymptotic behavior of the MLEs. Four suitable lifetime data sets we engaged and modeled, to disclose the usefulness and the dominance of the MEK distribution over its participant models.