In this research, the semiparametric Bayesian method is compared with the classical  method to  estimate reliability function of three  systems :  k-out of-n system, series system, and parallel system. Each system consists of three components, the first one represents the composite parametric in which failure times distributed as exponential, whereas the second and the third components are nonparametric ones in which reliability estimations depend on Kernel method using two methods to estimate bandwidth parameter h method and Kaplan-Meier method. To indicate a better method for system reliability function estimation, it has be

In this study, we made a comparison between LASSO & SCAD methods, which are two special methods for dealing with models in partial quantile regression. (Nadaraya & Watson Kernel) was used to estimate the non-parametric part ;in addition, the rule of thumb method was used to estimate the smoothing bandwidth (h). Penalty methods proved to be efficient in estimating the regression coefficients, but the SCAD method according to the mean squared error criterion (MSE) was the best after estimating the missing data using the mean imputation method

The Dagum Regression Model, introduced to address limitations in traditional econometric models, provides enhanced flexibility for analyzing data characterized by heavy tails and asymmetry, which is common in income and wealth distributions. This paper develops and applies the Dagum model, demonstrating its advantages over other distributions such as the Log-Normal and Gamma distributions. The model's parameters are estimated using Maximum Likelihood Estimation (MLE) and the Method of Moments (MoM). A simulation study evaluates both methods' performance across various sample sizes, showing that MoM tends to offer more robust and precise estimates, particularly in small samples. These findings provide valuable insights into the ana

       Canonical correlation analysis is one of the common methods for analyzing data and know the relationship between two sets of variables under study, as it depends on the process of analyzing the variance matrix or the correlation matrix. Researchers resort to the use of many methods to estimate canonical correlation (CC); some are biased for outliers, and others are resistant to those values; in addition, there are standards that check the efficiency of estimation methods.

In our research, we dealt with robust estimation methods that depend on the correlation matrix in the analysis process to obtain a robust canonical correlation coefficient, which is the method of Biwe

Abstract:

Robust statistics Known as, resistance to errors caused by deviation from the stability hypotheses of the statistical operations (Reasonable, Approximately Met, Asymptotically Unbiased, Reasonably Small Bias, Efficient ) in the data selected in a wide range of probability distributions whether they follow a normal distribution or a mixture of other distributions deviations different standard .

power spectrum function lead to, President role in the analysis of Stationary random processes, form stable random variables organized according to time, may be discrete random variables or continuous. It can be described by measuring its total capacity as function in frequency.

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 إن المقصود باختبارات حسن المطابقة هو التحقق من فرضية العدم القائمة على تطابق مشاهدات أية عينة تحت الدراسة لتوزيع احتمالي معين وترد مثل هكذا حالات في التطبيق العملي بكثرة وفي كافة المجالات وعلى الأخص بحوث علم الوراثة والبحوث الطبية والبحوث الحياتية ,عندما اقترح كلا من   Shapiro والعالم Wilk  عام 1965 اختبار حسن المطابقة الحدسي مع معالم القياس
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This paper deals  with constructing mixed probability distribution  from exponential with scale parameter (β) and also Gamma distribution with (2,β), and the mixed proportions are (  .first of all, the probability density function (p.d.f) and also cumulative distribution function (c.d.f) and also the reliability function are obtained. The parameters of mixed distribution, ( ,β)  are estimated by three different methods, which are  maximum likelihood, and  Moments method,as well proposed method (Differential Least Square Method)(DLSM).The comparison is done using simulation procedure, and all the results are explained in tables.

Segmented regression consists of several sections separated by different points of membership, showing the heterogeneity arising from the process of separating the segments within the research sample. This research is concerned with estimating the location of the change point between segments and estimating model parameters, and proposing a robust estimation method and compare it with some other methods that used in the segmented regression. One of the traditional methods (Muggeo method) has been used to find the maximum likelihood estimator in an iterative approach for the model and the change point as well. Moreover, a robust estimation method (IRW method) has used which depends on the use of the robust M-estimator technique in

Abstract:

      In this research we discussed the parameter estimation and variable selection in Tobit quantile regression model in present of multicollinearity problem. We used elastic net technique as an important technique for dealing with both multicollinearity and variable selection. Depending on the data we proposed Bayesian Tobit hierarchical model with four level prior distributions . We assumed both tuning parameter are random variable and estimated them with the other unknown parameter in the model .Simulation study was used for explain the efficiency of the proposed method and then we compared our approach with (Alhamzwi 2014 & standard QR) .The result illustrated that our approach