Estimation of Stress-Strength model in the Generalized Linear Failure Rate Distribution

In this paper, we study the estimation of $R=P [Y < X ]$, also so-called the stress-strength model, when both $X$ and $Y$ are two independent random variables with the generalized linear failure rate distributions, under different assumptions about their parameters. We address the maximum likelihood estimator (MLE) of $R$ and the associated asymptotic confidence interval. In addition, we compute the MLE and the corresponding Bootstrap confidence interval when the sample sizes are small. The Bayes estimates of $R$ and the associated credible intervals are also investigated. An extensive computer simulation is implemented to compare the performances of the proposed estimators. Eventually, we briefly study the estimation of this model when the data obtained from both distributions are progressively type-II censored. We present the MLE and the corresponding confidence interval under three different progressive censoring schemes. We also analysis a set of real data for illustrative purpose.Comment: 31 pages, 2 figures, preprin

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

Preference of Estimation Approach for Rayleigh Progressive Type II Data

This paper compare the performance of the empirical Bayes and generalized maximum likelihood estimation approaches in context of progressively Type II censored data from one parameter Rayleigh distribution. The generalized maximum likelihood and empirical Bayes estimates of scale parameter, reliability function, and failure rate function are compared using risk efficiency criterion. The empirical Bayes estimates are considered with respect to squared error loss function. The wind speed data is presented to illustrate the proposed estimation approaches, and an extensive Monte Carlo simulated study is done to compare the empirical Bayes and Generalized maximum likelihood estimates. The study indicates that the empirical Bayesian approach using squared error loss function is preferable than the generalized maximum likelihood approach for the estimation of reliability performances. Keywords: Progressively Type II censored samples, generalized maximum likelihood estimation, squared error loss function, empirical Bayes estimation, Risk efficiency, Monte Carlo simulation.

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

Exponentiated Rayleigh Distribution: A Bayes Study Using MCMC Approach Based on Unified Hybrid Censored Data

This paper aims to estimate the unknown parameters, survival and hazard functions for exponentiated Rayleigh distribution based on unfied hybrid censored data

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 of Weibull Extension Distribution under Imprecise Data

In this paper, we present the maximum likelihood (ML) and Bayes estimation of the unknown parameters, the reliability and hazard functions of the Weibull extension distribution based on progressively Type-II censoring scheme from fuzzy lifetime data. For the computation of Bayes estimates, we proposed using Tierney-Kadane’s approximation under square error and LINEX loss functions. The performance of the maximum likelihood and Bayes estimators compared in terms of their mean squared errors (MSEs) through the simulation study. The results indicated that MSEs based on Tierney-Kadane’s approximation are less than based on the ML method. Finally, to demonstrate the efficiency of the proposed methods, two real data sets are analyzed

Weibull-Linear Exponential Distribution and Its Applications

In this article, a new four-parameter lifetime distribution, namely, the Weibull-Linear exponential distribution is defined and studied. Several of its structural properties such as quartiles, moments, mean waiting time, mean residual lifetime, Renyi entropy, mode, and order statistics are derived. Based on the idea of the Weibull T − X family, the new density function of this model is developed. The model parameters, as well as some of the lifetime parameters (reliability and failure rate functions), are estimated using the maximum likelihood method. Asymptotic confidence intervals estimates of the model parameters are also evaluated by using the Fisher information matrix. Moreover, to construct the asymptotic confidence intervals of the reliability and failure rate functions, we need to find their variance of them, which are approximated by the delta method. A real data set is used to illustrate the application of the Weibull-Linear Exponential distribution