Hassen A. Muttlak’s research while affiliated with King Fahd University of Petroleum and Minerals and other places

Ranked set sampling (RSS) schemes were originally proposed to increase efficiency in estimation. On the other hand, group sequential methods provide substantial savings in sample and enable us to make decisions as early as possible. In this manuscript, we intend to combine the benefits of the two methodologies. We propose group sequential tests for one and two population means under RSS. We compare the power, average sample sizes and type I errors of the proposed tests to those of group sequential tests based on simple random sampling schemes. We illustrate the utility of the method by using data from HIV trial.

Ranked set sampling (RSS) is a technique for incorporating auxiliary (concomitant) information into estimation and testing procedures right at the design stage. In this paper, we propose group sequential testing procedures for comparing two treatments with binary outcomes under an RSS scheme with perfect ranking. We compare the power, the average sample sizes and type I errors of the proposed tests to those of the group sequential tests based on simple random sampling schemes. We illustrate the usefulness of the methodology by using data from a clinical trial on leukemia.

The purpose of this article is two-fold. First, we consider the ranked set sampling (RSS) estimation and testing hypothesis for the parameter of interest (population mean). Then, we suggest some alternative estimation strategies for the mean parameter based on shrinkage and pretest principles. Generally speaking, the shrinkage and pretest methods use the non-sample information (NSI) regarding that parameter of interest. In practice, NSI is readily available in the form of a realistic conjecture based on the experimenter’s knowledge and experience with the problem under consideration. It is advantageous to use NSI in the estimation process to construct improved estimation for the parameter of interest. In this contribution, the large sample properties of the suggested estimators will be assessed, both analytically and numerically. More importantly, a Monte Carlo simulation is conducted to investigate the relative performance of the estimators for moderate and large samples. For illustrative purposes, the proposed methodology is applied to a published data set.

A large-sample test for testing the equality of two population means based on ranked set samples is presented. The null and alternative distributions of the proposed test statistic are derived. The main theme here is to produce natural adaptive estimators with some desirable statistical properties. In the context of two arbitrary models, the expressions for the asymptotic mean squared error of the proposed estimators are presented and compared with the parallel expressions for the classical estimators. We demonstrate that the suggested preliminary test estimator has superior asymptotic mean squared error performance relative to the classical and pooled estimators. A simulation study and application of the methodology to real data are showcased.

Different confidence intervals (CI) will be constructed for the location and scale parameters of the logistic distribution by assuming that one of them is known. The maximum likelihood estimator and several different pivots will be used to construct different CI for the logistic parameters, using simple random sampling (SRS) and ranked set sampling (RSS). They will be compared via their expected lengths and the standard errors of their lengths using computer simulation. The CIs based on the RSS are found to be more efficient, i.e. having shorter expected lengths and smaller standard errors than their competitors based on the SRS.

In this study, we consider the application of the James–Stein estimator for population means from a class of arbitrary populations based on ranked set sample (RSS). We consider a basis for optimally combining sample information from several data sources. We succinctly develop the asymptotic theory of simultaneous estimation of several means for differing replications based on the well-defined shrinkage principle. We showcase that a shrinkage-type estimator will have, under quadratic loss, a substantial risk reduction relative to the classical estimator based on simple random sample and RSS. Asymptotic distributional quadratic biases and risks of the shrinkage estimators are derived and compared with those of the classical estimator. A simulation study is used to support the asymptotic result. An over-riding theme of this study is that the shrinkage estimation method provides a powerful extension of its traditional counterpart for non-normal populations. Finally, we will use a real data set to illustrate the computation of the proposed estimators.

In this article, we consider the median ranked set sampling estimation and test of hypothesis for the mean for symmetric distributions. We suggest some alternative estimation strategies for parameters based on shrinkage and pretest principles. It is advantageous to use the non-sample information in the estimation process to construct alternative estimations for the parameter of interest. In this article, large sample properties of the suggested estimators will be assessed numerically using computer simulation. The relative performance of the suggested estimators for moderate and large samples will also be simulated. For illustration purposes, the proposed methodology is applied using data collocated from the Pepsi Cola production company in Al-Khobar, Saudi Arabia.

The problem of making statistical inference about θ =P(X > Y) has been under great investigation in the literature using simple random sampling (SRS) data. This problem arises naturally in the area of reliability for a system with strength X and stress Y. In this study, we will consider making statistical inference about θ using ranked set sampling (RSS) data. Several estimators are proposed to estimate θ using RSS. The properties of these estimators are investigated and compared with known estimators based on simple random sample (SRS) data. The proposed estimators based on RSS dominate those based on SRS. A motivated example using real data set is given to illustrate the computation of the newly suggested estimators.

Auxiliary information is used along with ranking information to derive several classes of estimators to estimate the population mean of a variable of interest based on RSS (ranked set sample). The properties of these newly suggested estimators were examined. Comparisons between special cases of these estimators and other known estimators are made using a real data set. Some of the new estimators are superior to the old ones in terms of bias and mean square error.

In this paper, some test procedures for scale parameters of exponential and rectangular distributions involving the median ranked set sampling (MRSS) method are discussed. The necessary tables for the critical regions for the suggested tests are supplied. The power functions of the tests are compared with the power functions of the same tests suggested by Abu-Dayyeh and Muttlak (1996) using ranked set sampling (RSS) data. It is seen that the test procedures using the MRSS data have greater power than those using the RSS data when the sample is drawn from an exponential distribution.