Exponential distribution is one of most common distributions in studies and scientific researches with wide application in the fields of reliability, engineering and in analyzing survival function therefore the researcher has carried on extended studies in the characteristics of this distribution.

In this research, estimation of survival function for truncated exponential distribution in the maximum likelihood  methods and Bayes first and second method, least square method and Jackknife dependent in the first place on the maximum likelihood method, then on Bayes first method then comparing then using simulation, thus to accomplish this task, different size samples have been adopted by the searcher us

In this paper, Bayes estimators of Poisson distribution have been derived by using two loss functions: the squared error loss function and the proposed exponential loss function in this study, based on different priors classified as the two different informative prior distributions represented by erlang and inverse levy prior distributions and non-informative prior for the shape parameter of Poisson distribution. The maximum likelihood estimator (MLE) of the Poisson distribution has also been derived. A simulation study has been fulfilled to compare the accuracy of the Bayes estimates with the corresponding maximum likelihood estimate (MLE) of the Poisson distribution based on the root mean squared error (RMSE) for different cases of the

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

In this paper, the Monte-Carlo simulation method was used to compare the robust circular S estimator with the circular Least squares method in the case of no outlier data and in the case of the presence of an outlier in the data through two trends, the first is contaminant with high inflection points that represents contaminant in the circular independent variable, and the second the contaminant in the vertical variable that represents the circular dependent variable using three comparison criteria, the median standard error (Median SE), the median of the mean squares of error (Median MSE), and the median of the mean cosines of the circular residuals (Median A(k)). It was concluded that the method of least squares is better than the

The penalized least square method is a popular method to deal with high dimensional data ,where  the number of explanatory variables is large than the sample size . The properties of  penalized least square method are given high prediction accuracy and making estimation and variables selection

 At once. The penalized least square method gives a sparse model ,that meaning a model with small variables so that can be interpreted easily .The penalized least square is not robust ,that means very sensitive to the presence of outlying observation , to deal with this problem, we can used a robust loss function to get the robust penalized least square method ,and get robust penalized estimator and

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.

     The stress(Y) – strength(X) model reliability Bayesian estimation which defines life of a component with strength X and stress Y (the component fails if and only if at any time the applied stress is greater than its strength) has been studied, then the reliability; R=P(Y<X), can be considered as a measure of the component performance. In this paper, a Bayesian analysis has been considered for R when the two variables X and Y are independent Weibull random variables with common parameter α in order to study the effect of each of the two different scale parameters β and λ; respectively, using three different [weighted, quadratic and entropy] loss functions under two different prior functions [Gamma and extension of Jeffery

 إن المقصود باختبارات حسن المطابقة هو التحقق من فرضية العدم القائمة على تطابق مشاهدات أية عينة تحت الدراسة لتوزيع احتمالي معين وترد مثل هكذا حالات في التطبيق العملي بكثرة وفي كافة المجالات وعلى الأخص بحوث علم الوراثة والبحوث الطبية والبحوث الحياتية ,عندما اقترح كلا من   Shapiro والعالم Wilk  عام 1965 اختبار حسن المطابقة الحدسي مع معالم القياس
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Beta Distribution

Abstract

             Gamma and Beta Distributions has very important in practice in various areas of statistical and applications reliability and quality control of production. and There are a number of methods to generate data behave on according to these distribution. and These methods bassic primarily on the shape parameters of each distribution and the relationship between these distributions and their relationship with some other probability distributions.    &nb

     In this paper, some estimators for the unknown shape parameter and reliability function of Basic Gompertz distribution have been obtained, such as Maximum likelihood estimator and Bayesian estimators under Precautionary loss function using Gamma prior and Jefferys prior. Monte-Carlo simulation is conducted to compare mean squared errors (MSE) for all these estimators for the shape parameter and integrated mean squared error (IMSE's) for comparing the performance of the Reliability estimators. Finally, the discussion is provided to illustrate the results that summarized in tables.