The 3-parameter Weibull distribution is used as a model for failure since this distribution is proper when the failure rate somewhat high in starting operation and these rates will be decreased with increasing time .

In practical side a comparison was made between (Shrinkage and Maximum likelihood) Estimators for parameter and reliability function using simulation , we conclude that the Shrinkage estimators for parameters are better than maximum likelihood estimators but the maximum likelihood estimator for reliability function is the better using statistical measures (MAPE)and (MSE) and for different sample sizes.

Note:- n_s : small sample ; n_m=median sample

Generally, statistical methods are used in various fields of science, especially in the research field, in which Statistical analysis is carried out by adopting several techniques, according to the nature of the study and its objectives. One of these techniques is building statistical models, which is done through regression models. This technique is considered one of the most important statistical methods for studying the relationship between a dependent variable, also called (the response variable) and the other variables, called covariate variables. This research describes the estimation of the partial linear regression model, as well as the estimation of the “missing at random” values (MAR). Regarding the

This research deals with a shrinking method concerned with the principal components similar to that one which used in the multiple regression “Least Absolute Shrinkage and Selection: LASS”. The goal here is to make an uncorrelated linear combinations from only a subset of explanatory variables that may have a multicollinearity problem instead taking the whole number say, (K) of them. This shrinkage will force some coefficients to equal zero, after making some restriction on them by some "tuning parameter" say, (t) which balances the bias and variance amount from side, and doesn't exceed the acceptable percent explained variance of these components. This had been shown by MSE criterion in the regression case and the percent explained

This study relates to  the estimation of  a simultaneous equations system for the Tobit model where the dependent variables  ( )  are limited, and this will affect the method to choose the good estimator. So, we will use new estimations methods  different from the classical methods, which if used in such a case, will produce biased and inconsistent estimators which is (Nelson-Olson) method  and  Two- Stage limited dependent variables(2SLDV) method  to get of estimators that hold characteristics the good estimator .

That is , parameters will be estim

A sensitivity-turbidimetric method at (0-180^o) was used for detⁿ. of mebeverine in drugs by two solar cell and six source  with C.F.I.A.. The method was based on the formation  of  ion pair for the pinkish banana color  precipitate by the reaction of Mebeverine hydrochloride with Phosphotungstic acid. Turbidity was measured via the reflection of incident light that collides on the surface particles of   precipitated at 0-180^o. All variables were optimized. The linearity ranged of Mebeverine hydrochloride was 0.05-12.5mmol.L^-1, the L.D. (S/N= 3)(3S_B) was 521.92 ng/sample depending on dilution for the minimum concentration , with correlation coefficient r = 0.9966while was R.S.D%

The use of Bayesian approach has the promise of features indicative of regression analysis model classification tree to take advantage of the above information by, and ensemble trees for explanatory variables are all together and at every stage on the other. In addition to obtaining the subsequent information at each node in the construction of these classification tree. Although bayesian estimates is generally accurate, but it seems that the logistic model is still a good competitor in the field of binary responses through its flexibility and mathematical representation. So is the use of three research methods data processing is carried out, namely: logistic model, and model classification regression tree, and bayesian regression tree mode

The aim of this research is to use robust technique by trimming, as the analysis of maximum likelihood (ML) often fails in the case of outliers in the studied phenomenon. Where the (MLE) will lose its advantages because of the bad influence caused by the Outliers. In order to address this problem, new statistical methods have been developed so as not to be affected by the outliers. These methods have robustness or resistance. Therefore, maximum trimmed likelihood: (MTL) is a good alternative to achieve more results. Acceptability and analogies, but weights can be used to increase the efficiency of the resulting capacities and to increase the strength of the estimate using the maximum weighted trimmed likelihood (MWTL). In order to perform t

Abstract:

 This research aims to compare Bayesian Method and Full Maximum Likelihood to estimate hierarchical Poisson regression model.

The comparison was done by  simulation  using different sample sizes (n = 30, 60, 120) and different Frequencies (r = 1000, 5000) for the experiments as was the adoption of the  Mean Square Error to compare the preference estimation methods and then choose the best way to appreciate model and concluded that hierarchical Poisson regression model that has been appreciated Full Maximum Likelihood Full Maximum Likelihood  with sample size  (n = 30) is the best to represent the maternal mortality data after it has been reliance value param

          Simple, cheap, sensitive, and accurate kinetic- spectrophotometric method has been developed for the determination of naringenin in pure and supplements formulations. The method is based on the formation of Prussian blue. The product dye exhibits a maximum absorbance at 707 nm. The calibration graph of naringenin was linear over the range 0.3 to 10 µg ml^-1 for the fixed time method (at 15 min) with a correlation coefficient (r) and percentage linearity (r²%) were of 0.9995 and 99.90 %, respectively, while the limit of detection LOD was 0.041 µg ml^-1. The method was successfully applied for the determination of naringenin in supplements with satisfac

In this research the Empirical Bayes method is used to Estimate the affiliation parameter in the clinical trials and then we compare this with the Moment Estimates for this parameter using Monte Carlo stimulation , we assumed that the distribution of the observation is binomial distribution while the distribution with the unknown random parameters is beta distribution ,finally we conclude that the Empirical bayes method for the random affiliation parameter is efficient using Mean Squares Error (MSE) and for different Sample size .