In this study, the stress-strength model R = P(Y < X < Z)  is discussed as an important parts of reliability system by assuming that the random variables follow Invers Rayleigh Distribution. Some traditional estimation methods are used    to estimate the parameters  namely; Maximum Likelihood, Moment method, and Uniformly Minimum Variance Unbiased estimator and Shrinkage estimator using three types of shrinkage weight factors. As well as, Monte Carlo simulation are used to compare the estimation methods based on mean squared error criteria.  

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, 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 presents a grey model GM(1,1) of the first rank and a variable one and is the basis of the grey system theory , This research dealt  properties of grey model and a set of methods to estimate parameters of the grey model GM(1,1)  is the least square Method (LS) , weighted least square method (WLS), total least square method (TLS) and gradient descent method  (DS). These methods were compared based on two types of standards: Mean square error (MSE), mean absolute percentage error (MAPE), and after comparison using simulation the best method was applied to real data represented by the rate of consumption of the two types of oils a Heavy fuel (HFO) and diesel fuel (D.O) and has been applied several tests to

            Ibn al-Haytham is the pioneer of optics, which is a science that had described optics circumstances. Optics or landscape science as it was known by the Arab and Muslim scientists at the time when  is a science known as the conditions of sighters in their quantity and quality as the proximity and distance from the beholder , the different forms , conditions and what mediate between the beholder and the microscopes , to explain useful knowledge of what obscures the sight of the conditions of sighters and is used to measure the space Distant criminality and  mirrors.

Ibn al-Haitham wrote his famous book The Book of Mirrors and studied mistakes adopted the m

The present work aims to study the treatment of oily wastewater by means of forward osmosis membrane bioreactor process. Side stream (external) configuration and submerged (internal) configuration of osmotic membrane bioreactor were performed and investigated. The experimental work for each configuration was carried out continuously over 21 days. The flux behavior of forward osmosis membrane in an osmotic membrane bioreactor (OMBR) was investigated, using NaCl as the draw solution and CTA as FO membrane. The effect of mixed liquor suspended solids (MLSS) concentration and TDS accumulation of bioreactor on water flux and membrane fouling behaviors was detected. The accumulation and rejection of nutrients in the bioreactor (Nitrate, COD,

Objective: An efficient solution for stabilization is the mobilization of the joints for the arthrokinematics affected by the positional defect of the CAI (i.e. chronic ankle instability). This study put to comparison the impacts of ankle dorsi flexion range of motion (DFROM) as well as dynamic balance ability (DBA) in the patients who have CAI using PJM (i.e. passive joint mobilization), a technique typically been used in previous works, and active joint mobilization (AJM), a technique which could have a greater impact on cortical excitability with the spontaneous movement. Design: rehabilitation program to treat recurrent ankle. Methods: A total of 10 players from the Iraqi clubs Muay Thai team were registered, 5 from each of