Reliability estimation for the randomly censored pareto distribution

Widespread applications of random censoring in life testing experiments to estimate reliability of engineering products or systems are avialable. Different parametric statistical models such as exponential, Rayleigh, Weibull and Maxwell distributions are used under random censoring scheme. In this paper, random censoring under Pareto distribution is considered. The maximum likelihood estimators (MLE’s) of the model parameters and survival function were derived along with Fisher information matrix and asymptotic confidence intervals. A simulation study was performed to observe the behavior of the MLE’s. The simulation results showed that the bias and MSE were reasonably small in all cases

Change Point Estimation for Pareto Type-II Model

Some Bayes estimators of the change point for the Pareto Type-II model under right item failure-censoring scheme are proposed. The Bayes estimators are obtained here in two cases, the first is when one parameter is known and second when both parameters are considered as the random variable. The performances of the procedures are illustrated by simulation technique

Hierarchical Bayes Estimation of Reliability Indexes of Cold Standby Series System under General Progressive Type II Censoring Scheme

In this paper, hierarchical Bayes approach is presented for estimation and prediction of reliability indexes and remaining lifetimes of a cold standby series system under general progressive Type II censoring scheme. A simulation study has been carried out for comparison purpose. The study will help reliability engineers in various industrial series system setups

Non-Bayes, Bayes and Empirical Bayes Estimators for the Shape Parameter of Lomax Distribution

Point estimation is one of the core topics in mathematical statistics. In this paper we consider the most common methods of point estimation: non-Bayes, Bayes and empirical Bayes methods to estimate the shape parameter of Lomax distribution based on complete data. The maximum likelihood, moment and uniformly minimum variance unbiased estimators are obtained as non-Bayes estimators. Bayes and empirical Bayes estimators are obtained corresponding to three informative priors "gamma, chi-square and inverted Levy" based on symmetric "squared error" and asymmetric "LINEX and general entropy" loss functions. The estimates of the shape parameter were compared empirically via Monte Carlo simulation study based upon the mean squared error. Among the set of conclusions that have been reached, it is observed that, for all sample sizes and different cases, the performance of uniformly minimum variance unbiased estimator is better than other non-Bayes estimators. Further that, Monte Carlo simulation results indicate that the performance of Bayes and empirical Bayes estimator in some cases are better than non-Bayes for some appropriate of prior distribution, loss function, values of parameters and sample size. Keywords: Lomax distribution; maximum likelihood estimator; moment estimator; uniformly minimum variance unbiased estimator; Bayes estimator; empirical Bayes estimator; informative prior; squared error loss function; LINEX  loss  function;  general  entropy  loss  function;  mean  squared  error

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

E-Bayesian estimation for the Lomax distribution based on type-II censored data

AbstractThis paper is concerned with using the E-Bayesian method for computing estimates of the unknown parameter and some survival time parameters e.g. reliability and hazard functions of Lomax distribution based on type-II censored data. These estimates are derived based on a conjugate prior for the parameter under the balanced squared error loss function. A comparison between the new method and the corresponding Bayes and maximum likelihood techniques is conducted using the Monte Carlo simulation