In this paper, we have derived Bayesian estimation for the parameters and reliability function of Perks distribution based on two different loss functions, Lindley’s approximation has been used to obtain those values. It is assumed that the parameter behaves as a random variable have a Gumbell Type P prior with non-informative is used. And after the derivation of mathematical formulas of those estimations, the simulation method was used for comparison depending on mean square error (MSE) values and integrated mean absolute percentage error (IMAPE) values respectively. Among of conclusion that have been reached, it is observed that, the LE-NR estimate introduced the best perform for estimating the parameter λ.

The acceptance sampling plans for generalized exponential distribution, when life time experiment is truncated at a pre-determined time are provided in this article. The two parameters (α, λ), (Scale parameters and Shape parameters) are estimated by LSE, WLSE and the Best Estimator’s for various samples sizes are used to find the ratio of true mean time to a pre-determined, and are used to find the smallest possible sample size required to ensure the producer’s risks, with a pre-fixed probability (1 - P^*). The result of estimations and of sampling plans is provided in tables.

Key words: Generalized Exponential Distribution, Acceptance Sampling Plan, and Consumer’s and Producer Risks

In this paper, we proposed a new class of Weighted Rayleigh Distribution based on two parameters, one is scale parameter and the other is shape parameter which introduced in Rayleigh distribution. The main properties of this class are derived and investigated in . The moment method and maximum likelihood method are used to obtain estimators of parameters, survival function and hazard function. Real data sets are collected to investigate two methods which depend it in this study. A comparison was made between two methods of estimation.

 In this study, we derived the estimation for Reliability of the Exponential distribution based on the Bayesian approach. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .We  derived  posterior distribution the parameter of the Exponential distribution under four types priors distributions for the scale parameter of the Exponential distribution is: Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. And the estimators for Reliability is obtained using the two proposed loss function in this study which is based on the natural logarithm for Reliability function .We used simulation technique, to compare the

      Long memory analysis is one of the most active areas in econometrics and time series where various methods have been introduced to identify and estimate the long memory parameter in partially integrated time series. One of the most common models used to represent time series that have a long memory is the ARFIMA (Auto Regressive Fractional Integration Moving Average Model) which diffs are a fractional number called the fractional parameter. To analyze and determine the ARFIMA model, the fractal parameter must be estimated. There are many methods for fractional parameter estimation. In this research, the estimation methods were divided into indirect methods, where the Hurst parameter is estimated fir

This paper is interested in comparing the performance of the traditional methods to estimate parameter of exponential distribution (Maximum Likelihood Estimator, Uniformly Minimum Variance Unbiased Estimator) and the Bayes Estimator in the case of data to meet the requirement of exponential distribution and in the case away from the distribution due to the presence of outliers (contaminated values). Through the employment of simulation (Monte Carlo method) and the adoption of the mean square error (MSE) as criterion of statistical comparison between the performance of the three estimators for different sample sizes ranged between small, medium and large        (n=5,10,25,50,100) and different cases (wit

The research dealt with a comparative study between some semi-parametric estimation methods to the Partial linear Single Index Model using simulation. There are two approaches to model estimation two-stage procedure and MADE to estimate this model. Simulations were used to study the finite sample performance of estimating methods based on different Single Index models, error variances, and different sample sizes , and the mean average squared errors were used as a comparison criterion between the methods were used. The results showed a preference for the two-stage procedure depending on all the cases that were used

Many of the dynamic processes in different sciences are described by models of differential equations. These models explain the change in the behavior of the studied process over time by linking the behavior of the process under study with its derivatives. These models often contain constant and time-varying parameters that vary according to the nature of the process under study in this We will estimate the constant and time-varying parameters in a sequential method in several stages. In the first stage, the state variables and their derivatives are estimated in the method of penalized splines(p- splines) . In the second stage we use pseudo lest square to estimate constant parameters, For the third stage, the rem

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