Mohamed T. Madi

Bayesian inference for the generalized exponential distribution

The two-parameter generalized exponential (GE) distribution was introduced by Gupta and Kundu [Gupta, R.D. and Kundu, D., 1999, Generalized exponential distribution. Australian and New Zealand Journal of Statistics, 41(2), 173–188.]. It was observed that the GE can be used in situations where a skewed distribution for a nonnegative random variable is needed. In this article, the Bayesian estimation and prediction for the GE distribution, using informative priors, have been considered. Importance sampling is used to estimate the parameters, as well as the reliability function, and the Gibbs and Metropolis samplers data sets are used to predict the behavior of further observations from the distribution. Two data sets are used to illustrate the Bayesian procedure.

Emiratisation: determining the factors that influence the recruitment decisions of employers in the UAE

The Arab Gulfs labour market is being overhauled. The private sector is increasingly being ‘obliged’ to more actively support nationalisation programmes. This study seeks to quantitatively determine the recruitment decisions of the employers. We collated the views of just under 250 UAE-based HRM personnel, in order to identify which factors (social, cultural, economic, regulatory, educational and motivational) are most significant as cited in the relevant literature. Not having the necessary educational qualifications and high reservation wage demands were found to have less of a bearing than does the perceived lack of vocationally orientated motivation and the ambiguities over the differing rights afforded to employees.

Estimation of P(Y < X) for the Three-Parameter Generalized Exponential Distribution

This article considers the estimation of R = P(Y < X) when X and Y are distributed as two independent three-parameter generalized exponential (GE) random variables with different shape parameters but having the same location and scale parameters. A modified maximum likelihood method and a Bayesian technique are used to estimate R on the basis of independent complete samples. The Bayes estimator cannot be obtained in explicit form, and therefore it has been determined using an importance sampling procedure. An analysis of a real life data set is presented for illustrative purposes.

Bayesian prediction of the total time on test using doubly censored rayleigh data

In a Bayesian setting, and on the basis of a doubly censored random sample of failure times drawn from a Rayleigh distribution, Fernandez (2000, Statist. Probab. Lett. , 48 , 393-399) considered the problem of predicting an independent future sample from the same distribution. In this article, we extend his work to include the estimation of the predictive distribution of the total time on test up to a certain failure in a future sample, as well as that of the remaining testing time time until all the items in the original sample have failed. Two examples are used to illustrate the prediction procedure.

Multiple step-stress accelerated life test: the tampered failure rate model

Battacharyya and Soejoeti (1989) proposed the tampered failure rate model for step-stress accelerated life testing. In this note, their model is generalized from the simple (2-step) step-stress setting to the multiple (k-step, k > 2) setting. For the parametric setting where the life distribution under constant stress is Weibull, maximum likelihood estimation is investigated and the situation where the different stress levels are equispaced is looked at.

Bayesian Inference for the Generalized Exponential Distribution Based on Progressively Censored Data

Based on a progressively Type-II censored sample, Bayesian estimation of the parameters as well as Bayesian prediction of the unobserved failure times from the generalized exponential (GE) distribution are studied. Importance sampling is used to estimate the scale and shape parameters. The Gibbs and Metropolis samplers are considered for predicting times to failure of units in multiple stages. A numerical simulation study involving three data sets is presented to illustrate the methods of estimation and prediction.

Bayesian inference for partially accelerated life tests using Gibbs sampling

Abstract We consider a life testing situation in which several groups of items are put, at different instances, on the partially accelerated life test proposed by DeGroot and Goel [Naval Research Logistics Quarterly, 1979. 26, 223–235]. The combined failure time data are then used to derive empirical Bayes estimators for the failure of the exponential life length under normal conditions. The estimation which is implemented using the Gibbs sampler Monte-Carlo-based approach, illustrates once again the ease with which these new types of estimation problems often requiring sophisticated numerical or analytical expertise, can be handled using the sampling based approach.

Bayesian estimation for shifted exponential distributions

Abstract Consider m random samples which are independently drawn from m shifted exponential distributions, with respective location parameters θ1, θ2, …, θm and common scale parameter σ. On the basis of the given samples and in a Bayesian framework, we address the problem of estimating the scale parameter σ and the parametric function γ = ∑mi=1 aiθi + bσ. Our proposed Bayesian estimators are compared, via a Monte Carlo study, to the invariant estimators proposed by Madi and Tsui (1990) and Rukhin and Zidek (1985) in terms of risk improvements on the best affine equivariant estimators.

On the invariant estimation of an exponential scale using doubly censored data

We consider the problem of estimating the scale parameter [theta] of the shifted exponential distribution with unknown shift based on a doubly censored sample from this distribution. Under squared error loss, Elfessi (Statist. Probab. Lett. 36 (1997) 251) has shown that the best affine equivariant estimator (BAEE) of [theta] is inadmissible. A smoother dominating procedure is proposed. The new improved estimator is shown, via a numerical study, to provide more significant risk reductions over the BAEE.

On the invariant estimation of a normal variance ratio

Abstract We consider the estimation of the variance ratio of two normal populations with unknown means. Two smooth estimators that improve on the best affine equivariant estimator (BAEE), under a large class of bowl-shaped loss functions, are derived. A numerical study is performed to get a feel for the magnitude of risk reduction when these estimators are used instead of the BAEE.