The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the <

Discriminant analysis is a technique used to distinguish and classification an individual to a group among a number of  groups based on a linear combination of a set of relevant variables know discriminant function. In this research  discriminant analysis used to analysis data from repeated measurements design. We  will  deal  with the problem of  discrimination  and  classification in the case of  two  groups by assuming the Compound Symmetry covariance structure  under  the  assumption  of  normality for  univariate  repeated measures data.

In this article, we developed a new loss function, as the simplification of linear exponential loss function (LINEX) by weighting LINEX function. We derive a scale parameter, reliability and the hazard functions in accordance with upper record values of the Lomax distribution (LD). To study a small sample behavior performance of the proposed loss function using a Monte Carlo simulation, we make a comparison among maximum likelihood estimator, Bayesian estimator by means of LINEX loss function and Bayesian estimator using square error loss (SE) function. The consequences have shown that a modified method is the finest for valuing a scale parameter, reliability and hazard functions.

Abstract:                                        

   We can notice cluster data in social, health and behavioral sciences, so this type of data have a link between its observations and we can express these clusters through the relationship between measurements on units within the same group.

    In this research, I estimate the reliability function of cluster function by using the seemingly unrelate

The  role  of  free  radicals  generation  and  Lipid  Peroxidation

during the course of ischemic heart disease is well establshed as a basic for Pthogenesis and subsequent tissue damage consequenes . In an attempt to shed a light on the possible relationship between lipid peroxidation and some antioxidant.

The effect of vitamine E  (as a potent antioxidant free radical scavenger) . On the serum levels of the Lipoproteins, (HDLc) High Density Lipoprotein , (LDLc) Low Density Lipoprotein and (VLDLc) very Low Density Lipoprotein in healthy donors.

The  study  includes  (50) healthy  donors  from  males  and  females  ,

Fifty-four Sprague-Dawley albino adult male rats were classified into three main groups each of 18 rats treated for a particular duration (1,2, and 4) weeks respectively. Each group was subdivided into three subgroups each of six rats treated as follows; group (1) serve as normal control, group (2, and 3) intra-peritoneal treated with TiO₂NPs (50,200) mg/kg respectively, body *weight of all rats was measured before and after the experiment, then rats were dissected at the end of each experiment and the weights of the thyroid was measured. The result showed a highly significant decrease (p<0.01) in thyroid gland weight, a highly significant increase (p<0.01) in body weights and TSH, while a highly significant decrease (p&

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

The Log-Logistic distribution is one of the important statistical distributions as it can be applied in many fields and biological experiments and other experiments, and its importance comes from the importance of determining the survival function of those experiments. The research will be summarized in making a comparison between the method of maximum likelihood and the method of least squares and the method of weighted least squares to estimate the parameters and survival function of the log-logistic distribution using the comparison criteria MSE, MAPE, IMSE, and this research was applied to real data for breast cancer patients. The results showed that the method of Maximum likelihood best in the case of estimating the paramete