Ayman Baklizi

Shrinkage estimation of P(Y < X) in the exponential case

Abstract We consider the problem of estimating R = P(Y < X) where X and Y have independent exponential distributions with parameters θ and λ respectively. Assuming that there is a prior guess or estimate R 0, we develop various shrinkage estimators of R that incorporate this prior information. The performance of the new estimators is investigated and compared with the maximum likelihood estimator using Monte Carlo methods. It is found that some of these estimators are very successful in taking advantage of the prior estimate available. Recommendations concerning the use of these estimators are presented.

Inference about the mean of a skewed population: a comparative study

We consider the problem of hypotheses testing and interval estimation of the mean of a possibly skewed population. The usual procedures based on the large sample distribution of the studentized sample mean can be imprecise because of the violation of the nominal values of test sizes or confidence levels. Many attempts were made to overcome this problem. Most of them are based on correcting the studentized t-variable with higher order terms and possibly using the bootstrap to set critical values. Another approach is based on the empirical likelihood and possibly using the bootstrap or the Bartlett correction to improve the calibration. In this article, using simulation techniques, we investigate and compare these competing approaches in terms of the attainment of the nominal values of test sizes, confidence levels and the powers of the associated tests. It is found that intervals based on the Bartlett-corrected empirical likelihood are very accurate even for small sample sizes from highly skewed populations. Its power performance is also comparable and in many ways better than the other procedures considered, besides its applicability for testing when all other procedures fail to attain the nominal sizes of the tests.

Inference about the mean difference of two non-normal populations based on independent samples: a comparative study

Inference about the mean difference of two non-normal populations is considered. The usual procedures based on the large sample distribution of the t-test and various modifications of it as well as the approach based on the empirical likelihood are studied. The various procedures are compared using simulation techniques. The comparison was made in terms of the attainment of the nominal confidence levels, test sizes and powers. The results show that the bootstrapped empirical likelihood inference procedures are superior with accurate test sizes and confidence levels even for very small samples from considerably skewed, heavy-tailed or differently shaped parent populations.

Preliminary test estimation in the two parameter exponential distribution with time censored data

Given a prior guess of the unknown parameter @q, the preliminary test estimator based on the maximum likelihood estimator for the exponential scale parameter is developed. The optimal significance levels based on the minimax regret criterion and the corresponding critical values are obtained.

Asymptotic and Resampling-Based Confidence Intervals for P(X < Y)

ABSTRACT We consider asymptotic and resampling-based interval estimation procedures for the stress-strength reliability P(X < Y). We developed and studied several types of intervals. Their performances are investigated using simulation techniques and compared in terms of attainment of the nominal confidence level, symmetry of lower and upper error rates, and expected length. Recommendations concerning their use are given.

Shrinkage Estimation of the Common Location Parameter of Several Exponentials

Abstract Estimation of the common location parameter of several exponentials is considered. Using samples from m independent exponential populations with common location parameter θ, and given a prior guess θ0 of θ, several shrinkage estimators have been proposed that incorporate this prior information. We propose shrinkage factors by minimizing the mean squared error or utilizing the P-values obtained from combining certain independent statistics and tests. A simulation study is conducted to investigate the performance of the proposed estimators. It is found that the proposed estimators are effective in taking advantage of the available prior information.

Bayesian prediction intervals for ranges and waiting times

Abstract The problem of finding Bayesian prediction intervals for ranges and waiting times in exponential samples is considered. The intervals are derived assuming two kinds of prior distributions. Their performance in terms of their expected lengths is investigated using Monte Carlo methods. Comparisons are made between the derived intervals and the corresponding classical prediction intervals. The Bayesian intervals appear to be shorter.

Estimation of the Pareto scale parameter based on grouped data

Abstract We considered point estimation of the scale parameter of the Pareto distribution using grouped data. The maximum likelihood estimator in this situation has no closed form and requires an iterative numerical procedure. Several other estimators that exist in closed form are suggested. Their behavior is examined and compared with the maximum likelihood estimator under a variety of experimental conditions. The results show that some of the suggested estimators have statistical performance which is comparable with that of the maximum likelihood estimator.