Problem statement: The Weibull distribution has been widely used especially in the modeling of lifetime event data. It provides a statistical model which has a wide variety of applications in many areas, and the main advantage is its ability in the context of lifetime event, to provide reasonably accurate failure analysis and failure forecasts especially with extremely small samples. The conventional maximum likelihood method is the usual way to estimate the parameters of a distribution. Bayesian approach has received much attention and in contention with other estimation methods. In this study we explore and compare the performance of the maximum likelihood estimate with the Bayesian estimate for the Weibull distribution. Approach: The maximum likelihood estimation, Bayesian using Jeffrey prior and the extension of Jeffrey prior information for estimating the parameters of Weibull distribution of life time are presented. We explore the performance of these estimators numerically under varying conditions. Through the simulation study comparison are made on the performance of these estimators with respect to the Mean Square Error (MSE) and Mean Percentage Error (MPE). Results: For all the varying sample size, several specific values of the scale parameter of the Weibull distribution and for the values specify for the extension of Jeffrey prior, the estimators of the maximum likelihood method result in smaller MSE and MPE compared to Bayesian in majority of the cases. Nevertheless in all cases for both methods the MSE and MPE decrease as sample size increases. Conclusion: Based on the results of this simulation study the Bayesian approach used in the estimating of Weibull parameters is found to be not superior compared to the conventional maximum likelihood method with respect to MSE and MPE values

In this paper the Jeffery prior information and the extension of Jeffery prior information for estimating the parameter Weibull distribution is presented. Through simulation study the performance of this estimator was compared to the standard Bayes with Jeffery prior information with respect to the mean square error (MSE) and mean percentage error (MPE). In the results, The new estimator with extension of Jeffery prior information is the best estimator for Weibull Distribution, when compared it with standard Bayes with Jeffery prior information. Also depending on MSE and MPE, the is the best survival function for Weibull distribution when compared it with survival function based on posterior distribution. We can easily conclude that MSE and MPE of Bayes estimators decrease with an increase of sample size.

In this research, we applied actual data related to the number of infections with the Corona virus for some Arab countries for the month of February of the year 2022, where the method of least significant difference (LSD) was used to find out the significant differences in the number of infections between any two Arab countries. First, the completely random design method (CRD) was used to obtain a table of analysis of variance (ANOVA) and to know in general whether there are significant differences in the number of injuries between Arab countries or not, by rejecting the null hypothesis 𝐻 0 , the method of least significance LSD was used to compare the number of injuries between Arab countries (Is there a moral difference or not).

Problem statement: The main propose of this study was to evaluate the HIV patients for the period 1990-2008 depend on three variables age, gender and ethnicity. Approach: The data was analyzed using regression and correlation methods to get the mathematical model that explain the relationship and the effect between the age, gender and ethnicity. SSPS program V. 17.0 was used throughout this study to analyze the data and to generate the various Tables. Results: Using SPSS program to obtain regression models for each year in the period 1990-2008 depend on three variables age group, gender and ethnicity. Also obtained the relationship between all three variables in HIV patients using correlation methods. Conclusion: The age effect on gender and ethnicity in three years 1991, 2001 and 2002 are stronger than other years. In regression models, there exist significance effect between age and gender in two models, but there is no significance effect between age and ethnicity in all models. In correlation, there is no significance relationship between age and gender, age and ethnicity, ethnicity and genders in all years from 1990-2008

In this paper, we present the significant difference between the level of student comprehension for these year courses and for all student of mathematical department,college of science, Kufa university .Moreover to find out the effect of scientific, personality,ability of evaluation and ability of communication To have the goal ,we used some statistical methods like experimental design,correlation and regression analysis.