In this work, the methods (Moments, Modified Moments, L-Moments, Percentile, Rank Set sampling and Maximum Likelihood) were used to estimate the reliability function and the two parameters of the Transmuted Pareto (TP) distribution. We use simulation to generate the required data from three cases this indicates  sample size , and it replicates  for the real value for parameters, for reliability times values  we take .

Results were compared by using mean square error (MSE), the result appears as follows :

The best methods are Modified Moments, Maximum likelihood and L-Moments in first case, second case and third case respectively.

In this paper, some estimators for the unknown shape parameters and reliability function of Basic Gompertz distribution were obtained, such as Maximum likelihood estimator and some Bayesian estimators under Squared log error loss function by using Gamma and Jefferys priors. Monte-Carlo simulation was conducted to compare the performance of all estimates of the shape parameter and Reliability function, based on mean squared errors (MSE) and integrated mean squared errors (IMSE's), respectively. Finally, the discussion is provided to illustrate the results that are summarized in tables.

     In this paper, suggested formula as well a conventional method for estimating the twoparameters (shape and scale) of the Generalized Rayleigh Distribution was proposed. For different sample sizes (small, medium, and large) and assumed several contrasts for the two parameters a percentile estimator was been used. Mean Square Error was implemented as an indicator of performance and comparisons of the performance have been carried out through data analysis and computer simulation between the suggested formulas versus the studied formula according to the applied indicator. It was observed from the results that the suggested method which was performed for the first time (as far as we know), had highly advantage than t

The two parameters of Exponential-Rayleigh distribution were estimated using the maximum likelihood estimation method (MLE) for progressively censoring data. To find estimated values for these two scale parameters using real data for COVID-19 which was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. Then the Chi-square test was utilized to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). Employing the nonlinear membership function (s-function) to find fuzzy numbers for these parameters estimators. Then utilizing the ranking function transforms the fuzzy numbers into crisp numbers. Finally, using mean square error (MSE) to compare the outcomes of the survival

The aim of this study is to estimate the parameters and reliability function for kumaraswamy distribution of this two positive parameter  (a,b > 0), which is a continuous probability that has many characterstics with the beta distribution with extra advantages.

The shape of the function for this distribution and the most important characterstics are explained and estimated the two parameter (a,b) and the reliability function for this distribution by using the maximum likelihood method (MLE) and Bayes methods. simulation experiments are conducts to explain the behaviour of the estimation methods for different sizes depending on the mean squared error criterion the results show that the Bayes is bet

        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

In this paper, point estimation for parameter ? of Maxwell-Boltzmann distribution has been investigated by using simulation technique, to estimate the parameter by two sections methods; the first section includes Non-Bayesian estimation methods, such as (Maximum Likelihood estimator method, and Moment estimator method), while the second section includes standard Bayesian estimation method, using two different priors (Inverse Chi-Square and Jeffrey) such as (standard Bayes estimator, and Bayes estimator based on Jeffrey's prior). Comparisons among these methods were made by employing mean square error measure. Simulation technique for different sample sizes has been used to compare between these 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

      The aim of this paper is to estimate a single reliability system (R = P, Z > W) with a strength Z subjected to a stress W in a stress-strength model that follows a power Rayleigh distribution. It proposes, generates and examines eight methods and techniques for estimating distribution parameters and reliability functions. These methods are the maximum likelihood estimation(MLE), the exact moment estimation (EMME), the percentile estimation (PE), the least-squares estimation (LSE), the weighted least squares estimation (WLSE) and three shrinkage estimation methods (sh1) (sh2) (sh3). We also use the mean square error (MSE) Bias and the mean absolute percentage error (MAPE) to compare the estimation methods. Both theoretical c