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.

In this research estimated the parameters of Gumbel distribution Type 1 for Maximum values through the use of two estimation methods:- Moments (MoM) and Modification Moments(MM) Method. the Simulation used for comparison between each of the estimation methods to reach the best method to estimate the parameters where the simulation was to generate random data follow Gumbel distributiondepending on three models of the real values of the parameters for different sample sizes with samples of replicate (R=500).The results of the assessment were put in tables prepared for the purpose of comparison, which made depending on the mean squares error (MSE).

The 3-parameter Weibull distribution is used as a model for failure since this distribution is proper when the failure rate somewhat high in starting operation and these rates will be decreased with increasing time .

In practical side a comparison was made between (Shrinkage and Maximum likelihood) Estimators for parameter and reliability function using simulation , we conclude that the Shrinkage estimators for parameters are better than maximum likelihood estimators but the maximum likelihood estimator for reliability function is the better using statistical measures (MAPE)and (MSE) and for different sample sizes.

Note:- n_s : small sample ; n_m=median sample

This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela

This paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a₀) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge.

The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about beha

This paper demonstrates the construction of a modern generalized Exponential Rayleigh distribution by merging two distributions with a single parameter. The "New generalized Exponential-Rayleigh distribution" specifies joining the Reliability function of exponential pdf with the Reliability function of Rayleigh pdf, and then adding a shape parameter for this distribution. Finally, the mathematical and statistical characteristics of such a distribution are accomplished

The main aim of this paper is to study how the different estimators of the two unknown parameters (shape and scale parameter) of a generalized exponential distribution behave for different sample sizes and for different parameter values. In particular, 

. Maximum Likelihood, Percentile and Ordinary Least Square estimators had been implemented for different sample sizes (small, medium, and large) and assumed several contrasts initial values for the two parameters. Two indicators of performance Mean Square Error and Mean Percentile Error were used and the comparisons were carried out between different methods of estimation  by using monte carlo simulation technique .. It was obse

    The using of the parametric models and the subsequent estimation methods require the presence of many of the primary conditions to be met by those models to represent the population under study adequately, these prompting researchers to search for more flexible models of parametric models and these models were nonparametric models.

    In this manuscript were compared to the so-called Nadaraya-Watson estimator in two cases (use of fixed bandwidth and variable) through simulation with different models and samples sizes.  Through simulation experiments and the results showed that for the first and second models preferred NW with fixed bandwidth fo