In this research we study a variance component model, Which is the one of the most important models widely used in the analysis of the data, this model is one type of a multilevel models, and it is considered as linear models , there are three types of linear variance component models ,Fixed effect of linear variance component model, Random effect of linear variance component model and Mixed effect of linear variance component model . In this paper we will examine the model of mixed effect of linear variance component model with one –way random effect ,and the mixed model is a mixture of fixed effect and random effect in the same model, where it contains the parameter (μ) and treatment effect (τ_i ) which  has

A non-parametric kernel method with Bootstrap technology was used to estimate the confidence intervals of the system failure function of the log-normal distribution trace data. These are the times of failure of the machines of the spinning department of the weaving company in Wasit Governorate. Estimating the failure function in a parametric way represented by the method of the maximum likelihood estimator (MLE). The comparison between the parametric and non-parametric methods was done by using the average of Squares Error (MES) criterion. It has been noted the efficiency of the nonparametric methods based on Bootstrap compared to the parametric method. It was also noted that the curve estimation is more realistic and appropriate for the re

The use of non-parametric models and subsequent estimation methods requires that many of the initial conditions that must be met to represent those models of society under study are appropriate, prompting researchers to look for more flexible models, which are represented by non-parametric models                  

          In this study, the most important and most widespread estimations of the estimation of the nonlinear regression function were investigated using Nadaraya-Watson and Regression Local Ploynomial, which are one of the types of non-linear

             It is the regression analysis is the foundation stone of knowledge of statistics , which mostly depends on the ordinary least square method , but as is well known that the way the above mentioned her several conditions to operate accurately and the results can be unreliable , add to that the lack of certain conditions make it impossible to complete the work and analysis method and among those conditions are the multi-co linearity problem , and we are in the process of detected that problem between the independent variables using farrar –glauber test , in addition to the requirement linearity data and the lack of the condition last has been resorting to the

Soil water retention curves (SWRCs) are crucial for characterizing soil moisture dynamics and are particularly relevant in the context of irrigation management. A study was carried out to obtain the SWRC, inflection point, S index, pore size distribution curve, macro porosity, and air capacity from samples submitted to saturation and re-saturation processes. Five different-texture disturbed soil samples Sandy Loam, Loam, Sandy Clay Loam, Silt Loam, and Clay were collected. After obtaining SWRC, each air-dried soil samples were submitted to particle size distribution and clay dispersed in water analyses to verify the soil lost clay. The experimental design was completely randomized with three replications using two processes of SWRC (saturat

In this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.

Hard water does not pose a threat to human health but may cause precipitation of soap or results stone in the boilers. These reactions are caused by the high concentrations of Ca and Mg. In the industry they are undesirable because of higher fuel consumption for industrial use .Electromagnetic polarization water treatment is a method which can be used for increasing the precipitation of Ca ²⁺ and CO₃ ^2- ions in hard water to form CaCO₃ which leads to decrease the water hardness is research has been conducted by changing the number of coil turns and voltage of the system. The spectroscopy electron microscope was used for imaging the produced crystals. Results of the investigation indicated that