In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function i

We are used Bayes estimators for unknown scale parameter  when shape Parameter  is known of Erlang distribution. Assuming different informative priors for unknown scale  parameter. We derived The posterior density with posterior mean and posterior variance using different informative priors for unknown scale parameter  which are the inverse exponential distribution, the inverse chi-square distribution, the inverse Gamma distribution, and the standard Levy distribution as prior. And we derived Bayes estimators based on the general entropy loss function (GELF) is used the Simulation method to obtain the results. we generated different cases for the parameters of the Erlang model, for different sample sizes. The estimates have been comp

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

  This paper is concerned with Double Stage Shrinkage Bayesian (DSSB) Estimator for lowering the mean squared error of classical estimator ˆ q for the scale parameter (q) of an exponential distribution in a region (R) around available prior knowledge (q0) about the actual value (q) as initial estimate as well as to reduce the cost of experimentations.         In situation where the experimentations are time consuming or very costly, a Double Stage procedure can be used to reduce the expected sample size needed to obtain the estimator. This estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y( ) and for acceptance region R. Expression for

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.

The question of estimation took a great interest in some engineering, statistical applications, various applied, human sciences, the methods provided by it helped to identify and accurately the many random processes.

In this paper, methods were used through which the reliability function, risk function, and estimation of the distribution parameters were used, and the methods are (Moment Method, Maximum Likelihood Method), where an experimental study was conducted using a simulation method for the purpose of comparing the methods to show which of these methods are competent in practical application This is based on the observations generated from the Rayleigh logarithmic distribution (RL) with sample sizes

In this article, we developed a new loss function, as the simplification of linear exponential loss function (LINEX) by weighting LINEX function. We derive a scale parameter, reliability and the hazard functions in accordance with upper record values of the Lomax distribution (LD). To study a small sample behavior performance of the proposed loss function using a Monte Carlo simulation, we make a comparison among maximum likelihood estimator, Bayesian estimator by means of LINEX loss function and Bayesian estimator using square error loss (SE) function. The consequences have shown that a modified method is the finest for valuing a scale parameter, reliability and hazard functions.

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.

This paper deals with, Bayesian estimation of the parameters of Gamma distribution under Generalized Weighted loss function, based on 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 in terms of the mean squared errors (MSE’s).

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).