Mazen Nassar

Estimation of the inverse Weibull parameters under adaptive type-II progressive hybrid censoring scheme

This paper describes the frequentist and Bayesian estimation for the scale parameter λ and shape parameter β of the inverse Weibull (IW) distribution based on adaptive type-II progressive hybrid censoring scheme (AT-II PHCS). We discuss the maximum likelihood estimators (MLEs) and the approximate MLEs, where the MLEs cannot be obtained in closed forms. The Bayes estimates for the IW parameters are obtained based on squared error (SE) loss function by using the approximation form of Lindley (1980). The optimal censoring scheme has been suggested using two different optimality criteria. A real life data set is used for illustration purpose. Finally, the different proposed estimators have been compared through an extensive simulation studies.

Alpha power Weibull distribution: Properties and applications

ABSTRACT In this paper, a new lifetime distribution is defined and studied. We refer to the new distribution as alpha power Weibull distribution. The importance of the new distribution comes from its ability to model monotone and non monotone failure rate functions, which are quite common in reliability studies. Various properties of the proposed distribution are obtained including moments, quantiles, entropy, order statistics, mean residual life function, and stress-strength parameter. The maximum likelihood estimation method is used to estimate the parameters. Two real data sets are used to illustrate the importance of the proposed distribution.

A new extension of weibull distribution: Properties and different methods of estimation

Abstract The Weibull distribution has been generalized by many authors in recent years. Here, we introduce a new generalization of the Weibull distribution, called Alpha logarithmic transformed Weibull distribution that provides better fits than some of its known generalizations. The proposed distribution contains Weibull, exponential, logarithmic transformed exponential and logarithmic transformed Weibull distributions as special cases. Our main focus is the estimation from frequentist point of view of the unknown parameters along with some mathematical properties of the new model. The proposed distribution accommodates monotonically increasing, decreasing, bathtub and unimodal and then bathtub shape hazard rates, so it turns out to be quite flexible for analyzing non-negative real life data. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The potentiality of the distribution is analyzed by means of two real data sets.

Inference for Weibull distribution under adaptive Type-I progressive hybrid censored competing risks data

ABSTRACT In this paper, a competing risks model is considered under adaptive type-I progressive hybrid censoring scheme (AT-I PHCS). The lifetimes of the latent failure times have Weibull distributions with the same shape parameter. We investigate the maximum likelihood estimation of the parameters. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) techniques to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. To evaluate the performance of the estimators, a simulation study is carried out.

Alpha power transformed inverse Lindley distribution: A distribution with an upside-down bathtub-shaped hazard function

Abstract The inverse Lindley distribution has been generalized by many authors in recent years. Here, we introduce a new generalization called alpha power transformed inverse Lindley (APTIL) distribution that provides better fits than the inverse Lindley distribution and some of its known generalizations. The new model includes the inverse Lindley distribution as a special case. Various properties of the proposed distribution, including explicit expressions for the mode, moments, conditional moments, mean residual lifetime, Bonferroni and Lorenz curves, entropies, stochastic ordering, stress–strength reliability and order statistics are derived. The new distribution can have an upside-down bathtub failure rate function depending on its parameters. The model parameters are obtained by the method of maximum likelihood estimation. The approximate confidence intervals of the model parameters are also obtained. A simulation study is carried out to examine the performance of the maximum likelihood estimators of the parameters. Finally, two data sets have been analyzed to show how the proposed model works in practice.

Estimation and prediction of Marshall–Olkin extended exponential distribution under progressively type-II censored data

ABSTRACT In this paper, we consider Marshall–Olkin extended exponential (MOEE) distribution which is capable of modelling various shapes of failure rates and aging criteria. The purpose of this paper is three fold. First, we derive the maximum likelihood estimators of the unknown parameters and the observed the Fisher information matrix from progressively type-II censored data. Next, the Bayes estimates are evaluated by applying Lindley’s approximation method and Markov Chain Monte Carlo method under the squared error loss function. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We also compute 95% asymptotic confidence interval and symmetric credible interval along with the coverage probability. Third, we consider one-sample and two-sample prediction problems based on the observed sample and provide appropriate predictive intervals under classical as well as Bayesian framework. Finally, we analyse a real data set to illustrate the results derived.

A New Generalization of the Exponentiated Pareto Distribution With an Application

SYNOPTIC ABSTRACT We introduce for the first time a new lifetime distribution, namely, transmuted exponentiated Pareto (TEP) distribution, which generalizes the exponentiated Pareto distribution proposed by Gupta, Gupta, and Gupta (1998) with an additional parameter using the quadratic rank transmutation map which was studied by Shaw and Buckley (2009) to provide greater flexibility in modeling data from a practical point of view. In this article, our main focus is on estimation from a frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefly describe different estimation procedures, namely, the method of maximum likelihood estimation, moment estimation, L-moment estimation, least square and weighted least squares estimation, maximum product of spacings estimation, and Cramér-von-Mises estimation. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of one real data set.