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.

This study includes the application of non-parametric methods in estimating the conditional survival function of the Beran method using both the Nadaraya-Waston and the Priestley-chao weights and using data for Interval censored and Right censored of breast cancer and two types of treatment, Chemotherapy and radiation therapy Considering age is continuous variable, through using (MATLAB)  use of the (MSE) To compare weights The results showed a superior weight (Nadaraya-Waston) in estimating the survival function and condition of Both for chemotherapy and radiation therapy.

     Fuzzy C-means (FCM) is a clustering method used for collecting similar data elements within the group according to specific measurements. Tabu is a heuristic algorithm. In this paper, Probabilistic Tabu Search for FCM implemented to find a global clustering based on the minimum value of the Fuzzy objective function. The experiments designed for different networks, and cluster’s number the results show the best performance based on the comparison that is done between the values of the objective function in the case of using standard FCM and Tabu-FCM, for the average of ten runs.

     In this paper, Bayesian estimator for the parameter and reliability function of inverse Rayleigh distribution (IRD) were obtained Under three types of loss function, namely, square error loss function (SELF), Modified Square error loss function (MSELF) and Precautionary loss function (PLF),taking into consideration the  informative and non- informative  prior. The performance of such estimators was assessed on the basis of mean square error (MSE) criterion by performing a Monte Carlo simulation technique.

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

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

In this paper, the Decomposition method was used to find approximation solutions for a system of linear Fredholm integral equations of the second kind. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution, and Adomian decomposition method for solving linear and nonlinear integral equations. Finally, numerical examples are prepared to illustrate these considerations.

This deals with estimation of Reliability function and one shape parameter (?) of two- parameters Burr – XII , when ?(shape parameter is known) (?=0.5,1,1.5) and also the initial values of (?=1), while different sample shze n= 10, 20, 30, 50) bare used. The results depend on empirical study through simulation experiments are applied to compare the four methods of estimation, as well as computing the reliability function . The results of Mean square error indicates that Jacknif estimator is better than other three estimators , for all sample size and parameter values

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

Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calcula