Dr. Samira Faisal Hathoot Abushilah Al-Ghazi

This paper presents a method for determining the actual rank of the coefficients matrix in the reduced rank multivariate regression model. The method is constructed using the singular value decomposition and the Akaike's Information Criterion (AIC). Some illustrative examples are given to verify this method.

In this paper, we suggest an approach to estimate the probability density function for bivariate circular data. Kernel density estimation technique with different concentration parameters and different kernel functions are used to construct this approach. In our approach, we used Wrapped Cauchy distribution and Wrapped Normal distribution as a kernel function. Moreover, the procedure that we have suggested is applied to two types of data (simulated data and protein data). Firstly, we apply the approach that we have suggested to simulated data, which are generated from the bivariate von-Mises distribution, to highlight the joint probability density function for the bivariate von-Mises distribution. Secondly, the proposed approach is applied to real data, from the Protein Data Bank (PDB), to show the joint probability density function for some types of proteins.

Clustering amino acids is one of the most challenging problems in functional and structural prediction of protein. Previous studies have proposed clusters based on measurements of physical and biochemical characteristics of the amino acids such as volume, area, hydrophilicity, polarity, hydrogen bonding, shape, and charge. These characteristics, although important, are less directly related to the protein structure compared to geometrical characteristics such as dihedral angles between amino acids. We propose using the p-value from a test of equality of dihedral-angle distributions as the basis of a distance measure for the clustering. In this novel approach, an energy test is modified to deal with bivariate angular data and the p-value is obtained via a permutation method. The results indicate that the clusters of amino acids have sensible interpretation where Glycine, Proline, and Asparagine each forms a distinct cluster. A simulation study suggests that this approach has good working characteristics to cluster amino acids.

The object of the present paper is to develop a Bayesian fixed sample size procedure for selecting (choosing) the better of two Pascal populations (a version of Negative Binomial distribution that counts the number of trials at which the rth success occurs). The selection is made using Bayes risks under linear loss function, conjugate Beta priors and different sample sizes. Numerical results for this optimal Bayesian procedure are obtained and compared with those that obtained for a suboptimal procedure that based on posterior estimates.

In many practical situations the experimenter is confronted with the problem of choosing the best one of a number of populations or categories or ranking them according to their performance. This paper derives a procedure for selecting the better of Two Geometric populations employing a decision-theoretic Bayesian framework with Beta prior under general loss function .

In this paper an optimal (Bayesian) fixed sample size procedure for selecting the better of two Poisson populations is proposed and studied. Bayesian decision-theoretic approach with general loss function and Gamma priors are used to construct this procedure. The numerical result of this procedure are given with different loss functions constant, linear and quadratic, in one equation we can obtain the Bayes risk for the three types of the loss functions: constant, linear and quadratic. in this paper the numerical results are given by using Math Works Matlab ver. 7.10.0 .