Hani M. Samawi

On the Estimation of the Distribution Function Using Extreme and Median Ranked Set Sampling

We study relationships between extreme ranked set samples (ERSSs) and median ranked set sample (MRSS) with simple random sample (SRS). For a random variable X, we show that the distribution function estimator when using ERSSs and MRSS are more efficient than when using SRS and ranked set sampling for some values of a given x. n n n nIt is shown that using ERSSs can reduce the necessary sample size by a factor of 1.33 to 4 when estimating the median of the distribution. Asymptotic results for the estimation of the distribution function is given for the center of the distribution function. Data on the bilirubin level of babies in neonatal intensive care is used to illustrate the method.

On the efficiency of monte carlo methods using steady state ranked simulated samples

Samawi (1999) showed that the efficiency of Monte Carlo methods of integrals estimation can be substantially improved by using ranked simulated samples (RSIS) in place of uniform simulated samples (USIS). However, in this paper it is shown that substantial improvement of efficiency can be achieved further by using the steady state ranked simulated sample (SRSIS). It appears that the modified Monte Carlo methods using SRSIS provide unbiased and more efficient estimators for the integrals. Some theoretical properties of SRSIS are given. A simulation study is conducted to compare the performance of the methods using SRSIS with respect to USIS, for some examples.

THE EFFECT OF TRIFLUOPERAZINE ON THE GENOTOXICITY OF BLEOMYCIN IN CULTURED HUMAN LYMPHOCYTES

The effects of trifluoperazine on the toxicity and mutagenicity of bleomycin were examined in cultured human lymphocytes. Lymphocyte cultures were initiated from three adult healthy non-smoking male volunteers. Cultures were exposed to the drugs for either three or twenty hours prior to cell collection. The toxic and clastogenic effects of the different treatments were represented by the reduction in the mitotic indices and the induction of chromosomal aberrations (CA) respectively. Both TFP and BLM significantly increased CA frequencies and reduced the mitotic indices (MI) following all treatments. The reduction in the mitotic indices and the increase in CA frequencies induced by the combined administration of both BLM and TFP were highly significant (p ≤ 0.001), but they were not significantly different from the sum of those induced by the separate treatments with the two drugs. These combined treatments, however, potentiated the odds ratios compared to those of the separate drug treatments. Therefore, though the effect of TFP on the clastogenic and cytotoxic effects of BLM was additive, the observed potentiation of the odds ratios of the combined treatments compared to those of the separate treatments suggested a significant enhancement in the expected chemotherapeutic effects of BLM when administered with TFP.

More efficient monte carlo methods obtained by using ranked set simulated samples

Estimation of integrals by crude Monte Carlo methods, using uniform simulated sample (USS) required a large sample size to achieve high accuracy. Reduction in sample size is achieved using USS with the sophisticated Monte Carlo methods such as antithetic, importance or control variate sampling. In this paper, we show that the performance of these methods is substantially improved by using ranked simulated samples (RSIS) in place of USS. This results in a very large saving in of simulated sample size and hence in cost and time. We show that the modified methods using RSIS provide unbiased estimators for the integrals. Some characteristics and theoretical concepts of RSIS are given. A simulation study is conducted to compare the performance of the methods using RSIS to USS.

Power estimation for two-sample tests using importance and antithetic resampling

COLLINGS and HAMILTON (1988), described a uniform bootstrap method that is applied on observed or pilot data in order to approximate the power of the two-sample Wilcoxon test for location shift alternatives. In this paper we demonstrate how importance and antithetic resampling can be used to substantially reduce the amount of computation needed to approximate the power of the two-sample tests for location shift and scale alternatives. Importance and antithetic bootstrap resampling methods are applied to simulated data of different sample sizes from a variety of distributions as well as to data from the Iowa 65+ Rural Health Study. Also, a suggestion is given for using a combination of importance and antithetic resampling for approximating the power of two-sample tests.

Bivariate Sign Test for One-Sample Bivariate Location Model Using Ranked Set Sample

In this article, we introduce a bivariate sign test for the one-sample bivariate location model using a bivariate ranked set sample (BVRSS). We show that the proposed test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the non centrality parameter are derived. The asymptotic distribution of the vector of sample median as an estimator of the locations of the bivariate model is introduced. Theoretical and numerical comparisons of the asymptotic efficiency of the BVRSS sign test with respect to the BVSRS sign test are also given.

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.

Estimation of the Correlation Coefficient Using Bivariate Ranked Set Sampling with Application to the Bivariate Normal Distribution

Abstract Bivariate ranked set sampling BVRSS was introduced by Al-Saleh and Zheng (2002) as a bivariate version of the ordinary ranked set sampling (RSS). The procedure can be used when we deal with two characteristics simultaneously. In this article, the BVRSS procedure is used to estimate the correlation coefficient between two variables. The proposed estimators are compared to other existing estimators based on bivariate simple random sample BVSRS. The case of bivariate normal distribution is considered in details.

Power estimation for two sample tests using balanced resampling

Uniform bootstrap resampling as described by Efron(1979) and others is an assumption-free method that can be used for some inferential problems including power estimation for two-sample tests. However, it is inefficient, requiring thousands of replications to achieve any reasonable accuracy- The purpose of this paper is to extend the one-sample balanced resampling method put forward by Davison, Hinkley and Schechtman (1986) to two-sample problems and apply it to power estimation. This extension is tried on simulated data as well as on an real data from the Iowa 65+ Rural Health Study. The power of two-sample bootstrap Wilcoxon test and t-test is estimated for different location shift alternatives and sample sizes. The simulation studies show that the efficiency and reliability of the balanced resampling method are much better than that of the uniform resampling method. Also, the asymptotic theory gives the same results.

The role of importance sampling in the establishment of normal ranges for speech characteristics

Most measurements of voice characteristics have inherently skewed distributions that have never been characterized for individuals without speech disorders, that is, individuals with ‘‘normal’’ voices. Any diagnostic value these measures might have requires that one studies the characteristics of these ‘‘normal’’ voice distributions, in particular the quantiles necessary to establish the normal range. The focus will be on perturbations measures, such as jitter and shimmer. To solve this problem a method of importance sampling has been developed for estimating quantiles of skewed distributions. Importance sampling is a modified bootstrap procedure with exponential tilting, that is, a resampling method where the probabilities of the original observations appearing in the new samples are no longer equally weighted but are weighted by their closeness as an order statistic to the quantile being estimated. To estimate the normal limits of jitter and shimmer without resampling procedures will require at least 80...