Walid A. Abu-Dayyeh

Some estimators of a finite population mean using auxiliary information

In sample surveys, it is usual to make use of auxiliary information to increase the precision of estimators. Two classes of estimators are suggested to estimate the population mean for the variable of interest using two auxiliary variables. Some special cases of these two classes of estimators are considered and compared using real data set and computer simulation. It turns out that the newly suggested estimators dominate all other well-known estimators in terms of mean square error and bias. Finally we showed how to extend the two classes of estimators if more than two auxiliary variables are available.

A two server queue with Bernoulli schedules and a single vacation policy

In this paper, we study a two server queue with Bernoulli schedules and a single vacation policy. We have assumed Poisson arrivals waiting in a single queue and two parallel servers who provide heterogeneous exponential service to customers on first-come, first-served basis. We consider two models, in one we assume that after completion of a service both servers can take a vacation while in the other we assume that only one may take a vacation. The vacation periods in both models are assumed to be exponential. We obtain steady state probability generating functions of system size for various states of the servers. A particular case is discussed and a numerical example is provided.

More powerful sign test using median ranked set sample: Finite sample power comparison

Sign test using median ranked set samples (MRSS) is introduced and investigated. We show that, this test is more powerful than the sign tests based on simple random sample (SRS) and ranked set sample (RSS) for finite sample size. It is found that, when the set size of MRSS is odd, the null distribution of the MRSS sign test is the same as the sign test obtained by using SRS. The exact null distributions and the power functions, in case of finite sample sizes, of these tests are derived. Also, the asymptotic distribution of the MRSS sign tests are derived. Numerical comparison of the MRSS sign test power with the power of the SRS sign test and the RSS sign test is given. Illustration of the procedure, using real data set of bilirubin level in Jaundice babies who stay in neonatal intensive care is introduced.

Testing some hypotheses about the normal distribution using ranked set sample: a more powerful test

Abstract Ranked set sample (RSS) was introduced by McIntyre (1952) and by Takahasi and Wakimoto (1968) as a method of selecting data if the sampling units can be easily ranked without any cost, but it is very difficult or expensive to measure them. They proposed to use the RSS mean as an estimator for the population mean instead of the usual estimator which is the mean of the simple random sample (SRS). In this paper we consider testing some hypotheses about μ and σ2 of the normal distribution using RSS. It appears that the use of RSS gives much better results in terms of the power function compared to the SRS.

Weighted modified ranked set sampling methods

Many authors suggested several modifications for the ranked set sampling (RSS). McIntyre [Austral. J. Agricultural Res. 3 (1952) 385] and Samawi et al. [Biometrical J. 30 (1996) 577] suggested using the extreme ranked set sampling (ERSS). Sinha et al. [Statist. Decisions 14 (1996) 223] and Muttlak [J. Appl. Statist. Sci. 6 (1997)] suggested using the median ranked set sampling (MRSS). Another modification suggested by Muttlak [Modified ranked set sampling, Pak. J. Stat. (2003)] called percentile ranked set sampling (PRSS). Most of the estimators based on the modified ranked set sampling methods will be biased unless the underlining distribution is symmetric. To over come the bias problem in the modified RSS methods and to increase the efficiency of the estimators of the population mean for skewed distributions, weighted estimators are suggested. The weighted modified RSS estimators are compared with the unweighted modified RSS and the usual RSS estimator. It turns out that we can come up with unbiased estimators for the population mean, also we will improve upon the efficiency of the modified RSS and the RSS methods, for probability distributions considered in this study.

Logistic parameters estimation using simple random sampling and ranked set sampling data

Logistic distribution is very widely used in modeling real life problems in different fields of study, particularly in the area of reliability. In this study, we propose different estimators for the location and scale parameters using simple random sampling and ranked set sampling (RSS) or some modifications of RSS. The estimators are proposed in the cases of either one or both parameters are unknown. The estimators are compared with each other for the cases considered via their mean square error. Finally most of the estimators considered in this study are compared using real life example.

Weighted Extreme Ranked Set Sample for Skewed Population

Samawi et al. (1996) investigated the use of a variety of extreme ranked set samples (ERSSs) for estimating the population mean. They indicated that ERSSs give unbiased and more efficient estimators of the population mean , compared to simple random samples (SRSs), in case of symmetric distributions. Also, ERSSs are more practical than ranked set samples (RSSs) and reduce the ranking judgment error. However, ERSSs produce biased estimators for the population mean when the underlying distribution has a skewed shape. In this paper a generalization of ERSS namely the weighted extreme ranked set sample (WERSS) is suggested. WERSS gives an unbiased and more efficient estimate for the population mean of scale and location families of distributions, compared with SRS, using the same number of quantified units. Also, a sequential approach is introduced to estimate the population mean when a limited knowledge of the underlying distribution is available. Simulation as well as a real data example about the bilirubin level in jaundice neonatal babies are used to investigate and to illustrate the method.

Combining independent tests of triangular distribution

The problem of combining n independent tests, as n --> [is proportional to], for testing that the variables are uniformly distributed over the interval (0, 1) vs. that they have a triangular distribution with pdf will be studied. Six popular omnibus methods will be compared via Bahadur efficiency. It will be shown numerically that the sum of p-values method is the best among the methods studied.

Exact Bahadur slope for combining independent tests for normal and logistic distributions

Combining independent tests of hypotheses is an important and popular statistical practice. Usually, data about a certain phenomena come from different sources in different times, so we want to combine these data to study these phenomena. Several combination methods were used to combine infinity independent tests. These methods are Fisher, logistic, sum of P-values and inverse normal for testing simple hypotheses against one-sided alternative. These methods are compared via the exact Bahadur slope (EBS). These non-parametric methods depend on the P-value of the individual tests combined.

Local Power For Combining Independent Tests in The Presence of Nuisance Parameters For The Logistic Distribution

Four combination methods of independent tests for testing a simple hypothesis versus one-sided alternative are considered viz. Fisher, the logistic, the sum of P-values and the inverse normal method in case of logistic distribution. These methods are compared via local power in the presence of nuisance parameters for some values of α using simple random sample.