In this paper, we will illustrate a gamma regression model assuming that the dependent variable (Y) is a gamma distribution and that it's mean ( ) is related through a linear predictor with link function which is identity link function g(μ) = μ. It also contains the shape parameter which is not constant and depends on the linear predictor and with link function which is the log link and we will estimate the parameters of gamma regression by using two estimation methods which are The Maximum Likelihood and the Bayesian and a comparison between these methods by using the standard comparison of average squares of error (MSE), where the two methods were applied to real da

Baghdad city has been faced numerous issues related to freshwater environment deteriorations due to many reasons, mainly was the discharge of wastewater without adequate treatment. Al-Rustamiya Wastewater Treatment Plant (WWTP) have been constructed among many plants in Baghdad city to reduce the amount of wastewater discharged into natural environment and its subsequent adverse effects. This study was conducted to evaluate the performance of the plant which consist of a conventional activated sludge (CAS) and sequencing batch reactors (SBR) systems as secondary treatment units and its ability to meet Iraqi specifications. A reliability level determination and analysis also were conducted to find the plant's stability an

Baghdad city has been faced numerous issues related to freshwater environment deteriorations due to many reasons, mainly was the discharge of wastewater without adequate treatment. Al- Rustamiya Wastewater Treatment Plant (WWTP) have been constructed among many plants in Baghdad city to reduce the amount of wastewater discharged into natural environment and its subsequent adverse effects. This study was conducted to evaluate the performance of the plant which consist of a conventional activated sludge (CAS) and sequencing batch reactors (SBR) systems as secondary treatment units and its ability to meet Iraqi specifications. A reliability level determination and analysis also were conducted to find the plant's stability and its capabi

 In this study, we derived the estimation for Reliability of the Exponential distribution based on the Bayesian approach. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .We  derived  posterior distribution the parameter of the Exponential distribution under four types priors distributions for the scale parameter of the Exponential distribution is: Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. And the estimators for Reliability is obtained using the two proposed loss function in this study which is based on the natural logarithm for Reliability function .We used simulation technique, to compare the

In this paper, the error distribution function is estimated for the single index model by the empirical distribution function and the kernel distribution function. Refined minimum average variance estimation (RMAVE) method is used for estimating single index model. We use simulation experiments to compare the two estimation methods for error distribution function with different sample sizes, the results show that the kernel distribution function is better than the empirical distribution function.

This paper deals with the mathematical method for extracting the Exponential Rayleighh  distribution based on mixed between the cumulative distribution function of Exponential distribution and  the cumulative distribution function of Rayleigh distribution using an application (maximum), as well as derived different statistical properties for  distribution, and present a structure of a new distribution based on a modified weighted version of Azzalini’s (1985) named Modified Weighted Exponential Rayleigh  distribution such that this new distribution is generalization of the  distribution and provide some special models of the  distribution, as well as derived different statistical properties for  distribution

      The main problem when dealing with fuzzy data variables is that it cannot be formed by a model that represents the data through the method of Fuzzy Least Squares Estimator (FLSE) which gives false estimates of the invalidity of the method in the case of the existence of the problem of multicollinearity. To overcome this problem, the Fuzzy Bridge Regression Estimator (FBRE) Method was relied upon to estimate a fuzzy linear regression model by triangular fuzzy numbers. Moreover, the detection of the problem of multicollinearity in the fuzzy data can be done by using Variance Inflation Factor when the inputs variable of the model crisp, output variable, and parameters are fuzzed. The results were compared usin

This paper includes the application of Queuing theory with of Particle swarm algorithm or is called (Intelligence swarm) to solve the problem of The queues and developed for General commission for taxes /branch Karkh center in the service stage of the Department of calculators composed of six  employees , and it was chosen queuing model is a single-service channel  M / M / 1 according to the nature of the circuit work mentioned above and it will be divided according to the letters system for each employee, and  it was composed of data collection times (arrival time , service time, departure time)

     In this paper, Bayesian estimator for the parameter and reliability function of inverse Rayleigh distribution (IRD) were obtained Under three types of loss function, namely, square error loss function (SELF), Modified Square error loss function (MSELF) and Precautionary loss function (PLF),taking into consideration the  informative and non- informative  prior. The performance of such estimators was assessed on the basis of mean square error (MSE) criterion by performing a Monte Carlo simulation technique.

The uniform flow distrbiution in the multi-outlets pipe highly depends on the several parameters act togather. Therefor, there is no general method to achieve this goal. The  goal of this study is to investigate the proposed approach that can provide significant relief of the maldistribution. The method is based on re-circulating portion of flow from the end of the header to reduce pressure at this region . The physical model consists of main manifold with uniform longitudinal section having diameter of 152.4 mm (6 in), five laterals with diameter of 76.2 mm (3 in), and spacing of 300 mm. At first, The experiment is carried out with conventional manifold, which is a closed-end. Then, small amount of water is allowed