In the current study, the researchers have been obtained Bayes estimators for the shape and scale parameters of Gamma distribution under the precautionary loss function, assuming the priors, represented by Gamma and Exponential priors for the shape and scale parameters respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation.

Based on Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that, the performance of Bayes estimator under precautionary loss function with Gamma and Exponential priors is better than other estimates in all cases.

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, a new seven-parameter Mittag-Leffler function of a single com-plex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

One of the most important problems in the statistical inference is estimating parameters and Reliability parameter and also interval estimation , and testing hypothesis . estimating two parameters of exponential distribution and also reliability parameter in a stress-strength model.

This parameter deals with estimating the scale parameter and the Location parameter µ , of two exponential distribution   ,using moments estimator and maximum likelihood estimator , also we estimate the parameter R=pr(x>y), where x,y are two- parameter independent exponential random variables .

Statistical properties of this distribution and its properti

In this paper, Bayes estimators for the shape and scale parameters of Weibull distribution have been obtained using the generalized weighted loss function, based on Exponential priors. Lindley’s approximation has been used effectively in Bayesian estimation. Based on theMonte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s).

              The purpose of this project is to build a scientific base and computational programs in an accelerator design work. The transfer of group of laws in alinear accelerator cavity to computer codes written in Fortran power station language is inorder to get a numerical calculation of an electromagnetic field generated in the cavities of the linear accelerator. The program in put contains mainly the following, the geometrical cavity constant, and the triangular finite element method high – order polynomial. The out put contains vertical and horizontal components of the electrical field together with the electrical and the magnetic field intensity. 

Transforming the common normal distribution through the generated Kummer Beta model to the Kummer Beta Generalized Normal Distribution (KBGND) had been achieved. Then, estimating the distribution parameters and hazard function using the MLE method, and improving these estimations by employing the genetic algorithm. Simulation is used by assuming a number of models and different sample sizes. The main finding was that the common maximum likelihood (MLE) method is the best in estimating the parameters of the Kummer Beta Generalized Normal Distribution (KBGND) compared to the common maximum likelihood according to Mean Squares Error (MSE) and Mean squares Error Integral (IMSE) criteria in estimating the hazard function. While the pr

In this paper an estimator of reliability function for the pareto dist. Of the first kind has been derived and then a simulation approach by Monte-Calro method was made to compare the Bayers estimator of reliability function and the maximum likelihood estimator for this function. It has been found that the Bayes. estimator was better than maximum likelihood estimator for all sample sizes using Integral mean square error(IMSE).

In this paper, we proposed a new class of weighted Rayleigh distribution based on two parameters, scale and shape parameters which are introduced in Rayleigh distribution. The main properties of this class are investigated and derived.