This study includes Estimating scale parameter, location parameter  and reliability function  for Extreme Value (EXV) distribution by two methods, namely: -
- Maximum Likelihood Method (MLE).
- Probability Weighted Moments Method (PWM).

 Used simulations to generate the required samples to estimate the parameters and reliability function of different sizes(n=10,25,50,100) , and give real values for the parameters are and , replicate the simulation experiments (R_P=1000)

        In this paper, an estimate has been made for parameters and the reliability function for Transmuted power function (TPF) distribution through using some estimation methods as proposed new technique for white, percentile, least square, weighted least square and modification moment methods. A simulation was used to generate random data that follow the (TPF) distribution on three experiments (E₁ , E₂ , E₃)  of the real values of the parameters, and with sample size (n=10,25,50 and 100) and iteration samples (N=1000), and taking reliability times (0< t < 0) . Comparisons have been made between the obtained results from the estimators using mean square error (MSE). The results showed the

Abstract

   The extremes effects in parameters readings which are BOD (Biological Oxygen Demands) and DO(Dissolved Oxygen) can caused error estimating of the model’s parameters which used to determine the ratio of de oxygenation and re oxygenation of the dissolved oxygen(DO),then that will caused launch big amounts of the sewage pollution  water to the rivers and it’s turn is effect in negative form on the ecosystem life and the different types of the water wealth.

   As result of what mention before this research came to employees Streeter-Phleps model parameters estimation which are (K_d,K_r) the de oxygenation and re oxygenation ratios on respect

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 .

This work, deals with Kumaraswamy distribution. Kumaraswamy (1976, 1978) showed well known probability distribution functions such as the normal, beta and log-normal but in (1980) Kumaraswamy developed a more general probability density function for double bounded random processes, which is known as Kumaraswamy’s distribution. Classical maximum likelihood and Bayes methods estimator are used to estimate the unknown shape parameter (b). Reliability function are obtained using symmetric loss functions by using three types of informative priors two single priors and one double prior. In addition, a comparison is made for the performance of these estimators with respect to the numerical solution which are found using expansion method. The

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes est

     We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD)

In this paper we estimate the coefficients and scale parameter in linear regression model depending on the residuals are of type 1 of extreme  value distribution for the largest values . This can be regard as an improvement for the studies with the smallest values . We study two estimation methods ( OLS  & MLE ) where we resort to Newton – Raphson (NR) and Fisher Scoring methods to get MLE estimate because the difficulty of using the usual approach with MLE . The relative efficiency criterion is considered beside to the statistical inference procedures for the extreme value regression model of type 1 for largest values . Confidence interval , hypothesis testing for both scale parameter and regression coefficients

In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using   is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.

Maulticollinearity is a problem that always occurs when two or more predictor variables are correlated with each other. consist of the breach of one basic assumptions of the ordinary least squares method with biased estimates results, There are several methods which are proposed to handle this problem including the  method To address a problem  and  method To address a problem , In this research a comparisons are employed between the biased   method and unbiased   method with Bayesian   using Gamma distribution  method  addition to Ordinary Least Square metho