In this research, we find the Bayesian formulas and the estimation of Bayesian expectation for product system of Atlas Company.  The units of the system have been examined by helping the technical staff at the company and by providing a real data the company which manufacturer the system.  This real data include the failed units for each drawn sample, which represents the total number of the manufacturer units by the company system.  We calculate the range for each estimator by using the Maximum Likelihood estimator.  We obtain that the expectation-Bayesian estimation is better than the Bayesian estimator of the different partially samples which were drawn from the product system after  it checked by the

   The technology of reducing dimensions and choosing variables are very important topics in statistical analysis to multivariate. When two or more of the predictor variables are linked in the complete or incomplete regression relationships, a problem of multicollinearity are occurred which consist of the breach of one basic assumptions of the ordinary least squares method with incorrect estimates results.

 There are several methods proposed to address this problem, including the partial least squares (PLS), used to reduce dimensional regression analysis. By using linear transformations that convert a set of variables associated with a high link to a set of new independent variables and unr

Generalized Additive Model has been considered as a multivariate smoother that appeared recently in Nonparametric Regression Analysis. Thus, this research is devoted to study the mixed situation, i.e. for the phenomena that changes its behaviour from linear (with known functional form) represented in parametric part, to nonlinear (with unknown functional form: here, smoothing spline) represented in nonparametric part of the model. Furthermore, we propose robust semiparametric GAM estimator, which compared with two other existed techniques.

      In this paper we study and design two feed forward neural networks. The first approach uses radial basis function network and second approach uses wavelet basis function network to approximate the mapping from the input to the output space. The trained networks are then used in an conjugate gradient algorithm to estimate the output. These neural networks are then applied to solve differential equation. Results of applying these algorithms to several examples are presented

   In this paper, a Monte Carlo Simulation technique is used to compare the performance of the standard Bayes estimators of the reliability function of the one parameter exponential distribution .Three types of loss functions are adopted, namely, squared error  loss function (SELF) ,Precautionary error loss function (PELF) andlinear exponential error  loss function(LINEX) with informative and non- informative prior .The criterion integrated mean square error (IMSE) is employed to assess the performance of such estimators

Mixture experiments are response variables based on the proportions of component for this mixture. In our research we will compare the scheffʼe model with the kronecker model for the mixture experiments, especially when the experimental area is restricted.

     Because of the experience of the mixture of high correlation problem and the problem of multicollinearity between the explanatory variables, which has an effect on the calculation of the Fisher information matrix of the regression model.

     to estimate the parameters of the mixture model, we used the (generalized inverse ) And the Stepwise Regression procedure

The aim of our study is to solve a nonlinear epidemic model, which is the COVID-19 epidemic model in Iraq, through the application of initial value problems in the current study. The model has been presented as a system of ordinary differential equations that has parameters that change with time. Two numerical simulation methods are proposed to solve this model as suitable methods for solving systems whose coefficients change over time. These methods are the Mean Monte Carlo Runge-Kutta method (MMC_RK) and the Mean Latin Hypercube Runge-Kutta method (MLH_RK). The results of numerical simulation methods are compared with the results of the numerical Runge-Kutta 4th order method (RK4) from 2021 to 2025 using the absolute error, which prove

     In this paper, a Monte Carlo Simulation technique is used to compare the performance of MLE and the standard Bayes estimators of the reliability function of the one parameter exponential distribution.Two types of loss functions are adopted, namely, squared error  loss function (SELF) and modified square error loss function (MSELF) with informative and non- informative prior. The criterion integrated mean square error (IMSE) is employed to assess the performance of such estimators .

This research a study model of linear regression problem of autocorrelation of random error is spread when a normal distribution as used in linear regression analysis for relationship between variables and through this relationship can predict the value of a variable with the values of other variables, and was comparing methods (method of least squares, method of the average un-weighted, Thiel method and Laplace method) using the mean square error (MSE) boxes and simulation and the study included fore sizes of samples (15, 30, 60, 100). The results showed that the least-squares method is best, applying the fore methods of buckwheat production data and the cultivated area of the provinces of Iraq for years (2010), (2011), (2012),