Mohammad Al-Rawwash

On the Mx/G/1 queue with feedback and optional server vacations based on a single vacation policy

We study a single server queue with batch arrivals and general (arbitrary) service time distribution. The server provides service to customers, one by one, on a first come, first served basis. Just after completion of his service, a customer may leave the system or may opt to repeat his service, in which case this customer rejoins the queue. Further, just after completion of a customers service the server may take a vacation of random length or may opt to continue staying in the system to serve the next customer. We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average number of customers and the average waiting time in the queue. Some special cases of interest are discussed and some known results have been derived. A numerical illustration is provided.

An approach to setting up a national customer satisfaction index: the Jordan case study

The aim of this paper was to develop a national customer satisfaction index (CSI) in Jordan and to derive its theory using generalized maximum entropy. During the course of this research, we conducted two different surveys to complete the framework of this CSI. The first one is a pilot study conducted based on a CSI basket in order to select the main factors that comprise the Jordanian customer satisfaction index (JCSI). Based on two different analyses, namely nonlinear principal component analysis and factor analysis, the explained variances in the first and second dimensions were 50.32 and 16.99% respectively. Also, Cronbach coefficients α in the first and second dimensions were 0.923 and 0.521, respectively. The results of this survey suggests the inclusion of loyalty, complaint, expectation, image and service quality as the main CS factors of our proposed model. The second study is a practical implementation conducted on the Vocational Training Corporation in order to evaluate the proposed JCSI. The results indicated that the suggested components of the proposed model are significant and form a good fitted model. We used the comparative fit index and the normed fit index as goodness-of-fit measures to evaluate the effectiveness of our proposed model. Both measures indicated that the proposed model is a promising one.

Inference about the Regression Parameters Using Median-Ranked Set Sampling

The ranked set samples and median ranked set samples in particular have been used extensively in the literature due to many reasons. In some situations, the experimenter may not be able to quantify or measure the response variable due to the high cost of data collection, however it may be easier to rank the subject of interest. The purpose of this article is to study the asymptotic distribution of the parameter estimators of the simple linear regression model. We show that these estimators using median ranked set sampling scheme converge in distribution to the normal distribution under weak conditions. Moreover, we derive large sample confidence intervals for the regression parameters as well as a large sample prediction interval for new observation. Also, we study the properties of these estimators for small sample setup and conduct a simulation study to investigate the behavior of the distributions of the proposed estimators.

Gaussian estimation and joint modeling of dispersions and correlations in longitudinal data

Analysis of longitudinal, spatial and epidemiological data often requires modelling dispersions and dependence among the measurements. Moreover, data involving counts or proportions usually exhibit greater variation than would be predicted by the Poisson and binomial models. We propose a strategy for the joint modelling of mean, dispersion and correlation matrix of nonnormal multivariate correlated data. The parameter estimation for dispersions and correlations is based on the Whittles [P. Whittle, Gaussian estimation in stationary time series, Bull Inst. Statist. Inst. 39 (1962) 105-129.] Gaussian likelihood of the partially standardized data which eliminates the mean parameters. The model formulation for the dispersions and correlations relies on a recent unconstrained parameterization of covariance matrices and a graphical method [M. Pourahmadi, Joint mean-covariance models with applications to longitudinal data: unconstrained parameterization, Biometrika 86 (1999) 677-690] similar to the correlogram in time series analysis. We show that the estimating equations for the regression and dependence parameters derived from a modified Gaussian likelihood (involving two distinct covariance matrices) are broad enough to include generalized estimating equations and its many recent extensions and improvements. The results are illustrated using two datasets.

Covariance matrix estimation using repeated measurements when data are incomplete

Modeling repeated measurements data has been studied extensively lately in the parametric situation. However, it is significant to study the effect of various treatments over a period of time where the repeated measurements on the same subject are expected to be correlated. The correlation among the repeated measurements for all the subjects will be studied via the covariance matrix. The positive definite constraint is one of obstacles that encounters modeling the covariance structure, however the Cholesky decomposition removes this constraint and allows modeling the components of the covariance matrix [M. Pourahmadi, Joint mean-covariance models with applications to longitudinal data: unconstrained parameterization, Biometrika 86 (1999) 677-690]. In this paper, we adopt the estimation procedures introduced by Diggle and Verbyla [Nonparametric estimation of covariance structure in longitudinal data, Biometrics 54 (1998) 401-415] where the variogram cloud as well as the squared residuals are used to estimate the variogram and the variances via the kernel smoothing. Selecting the appropriate bandwidth value is one of the important steps in the estimation process, thus in our data analysis we choose the bandwidth using one of the most simple straight forward methods which is the cross-validation method developed by Rice and Silverman [Estimating the mean and covariance structure nonparametrically when the data are curves, J. Roy. Statist. Soc. B 53 (1991) 233-243] and adapted by others. Finally we apply these nonparametric techniques as well as a graphical method [M. Pourahmadi, Joint mean-covariance models with applications to longitudinal data: unconstrained parameterization, Biometrika 86 (1999) 677-690] to a real life data and use the penalized likelihood criterion like AIC and BIC to compare models of our interest. our interest.

Fisher information of the regression parameters using median ranked set sampling

We investigate the simple linear regression parameters estimates using median ranked set sampling where the ranking is performed on the response variable. We study the large sample properties of these estimators and derive the Fisher information matrix. Also, we derive the Maximum Likelihood Estimator (MLE)and present a simulation study to elaborate on the proposed estimators.

Modeling Covariance Parameters for Purely Autoregressive Correlated Longitudinal Data

Abstract In longitudinal data analysis, we usually introduce models for the response as well as the correlation among the repeated measurements. In this article, we present a method of modeling the variance-covariance parameters using the Gaussian estimating equation proposed by Whittle (1961) in the time series literature. Estimators are obtained by the direct differentiation of the Gaussian estimation function with respect to the variance-covariance parameters of interest where no distributional assumptions are made except for the first two moments. The Gaussian estimation method is applied to a simulated data in order to study the behavior of parameter estimates.