Estimating the survival and risk functions of a log-logistic distribution by using order statistics with practical application

The Log-Logistic distribution is one of the important statistical distributions as it can be applied in many fields ( biological, chemical and physical experiments) and its importance comes from the importance of determining the survival and risk function for these experiments. The research will work to determine the characteristics of the distribution through the use of order statistics to estimate its parameters using the approved standard Bayes method On the squared loss function (Bayslf) and determining the optimal method by comparing it with the MLE method according to a simulation method by taking different models for default values for parameter and different sample sizes and with MSE, IMSE comparison criteria as well as applying it to real data for breast cancer patients and determine survival and risk function