This research deals with a shrinking method concernes 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 v

Abstract:

One of the important things provided by fuzzy model is to identify the membership functions. In the fuzzy reliability applications with failure functions of the kind who cares that deals with positive variables .There are many types of membership functions studied by many researchers, including triangular membership function, trapezoidal membership function and bell-shaped membership function. In I research we used beta function. Based on this paper study classical method to obtain estimation fuzzy reliability function for both series and parallel systems.

In this paper, suggested method as well as the conventional methods (probability
plot-(p.p.) for estimations of the two-parameters (shape and scale) of the Weibull
distribution had proposed and the estimators had been implemented for different
sample sizes small, medium, and large of size 20, 50, and 100 respectively by
simulation technique. The comparisons were carried out between different methods
and sample sizes. It was observed from the results that suggested method which
were performed for the first time (as far as we know), by using MSE indicator, the
comparisons between the studied and suggested methods can be summarized
through extremely asymptotic for indicator (MSE) results by generating random
error

        This Research deals with estimation the reliability function for two-parameters Exponential distribution, using different estimation methods ; Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE) conclude that the shrinkage method perform better than the other methods

In this paper, some estimators of the unknown shape parameter and reliability function  of Basic Gompertz distribution (BGD) have been obtained, such as MLE, UMVUE, and MINMSE, in addition to estimating Bayesian estimators under Scale invariant squared error loss function assuming informative prior represented by Gamma distribution and non-informative prior by using Jefferys prior. Using Monte Carlo simulation method, these estimators of the shape parameter and R(t), have been compared based on mean squared errors and integrated mean squared, respectively

In this paper, we used maximum likelihood method and the Bayesian method to estimate the shape parameter (θ), and reliability function (R(t)) of the Kumaraswamy distribution with two parameters l , θ (under assuming the exponential distribution, Chi-squared distribution and Erlang-2 type distribution as prior distributions), in addition to that we used method of moments for estimating the parameters of the prior distributions. Bayes

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

      In this paper, a new class of ordinary differential equations is designed for some functions such as probability density function, cumulative distribution function, survival function and hazard function of power function distribution, these functions are used of the class under the study. The benefit of our work is that the equations ,which are generated from some probability distributions, are used to model and find  the  solutions  of problems in our lives, and that the solutions of these equations are a solution to these problems, as the solutions of the equations under the study are the closest and the most reliable to reality. The existence and uniqueness of solutions the obtained equations in the current study are dis

        In this paper, estimation of system reliability of the multi-components in stress-strength model R_(s,k) is considered, when the stress and strength are independent random variables and follows the Exponentiated Weibull Distribution (EWD) with known first shape parameter θ and, the second shape parameter α is unknown using different estimation methods. Comparisons among the proposed estimators through  Monte Carlo simulation technique were made depend on mean squared error (MSE)  criteria

In this paper, we derived an estimator of reliability function for Laplace distribution with two parameters using Bayes method with square error loss function, Jeffery’s formula and conditional probability random variable of observation. The main objective of this study is to find the efficiency of the derived Bayesian estimator compared to the maximum likelihood of this function and moment method using simulation technique by Monte Carlo method under different Laplace distribution parameters and sample sizes. The consequences have shown that Bayes estimator has been more efficient than the maximum likelihood estimator and moment estimator in all samples sizes