تقدير دالة المخاطرة الضبابية البيزية الحصينة لتوزيع كوشي المبتور مع تطبيق عملي

Rp-Estimation of the Robust Bayesian Fuzzy Hazard Function For a Truncated Cauchy Distribution with Practical Application.pdf

The process of estimating the risk function is one of the important topics that research and statistical studies focused on, and that these studies differ according to the methods used, whether they are traditional or Bayesian methods in order to obtain estimates with a high level of efficiency .
In this thesis, the focus was on the robust fuzzy Bayesian methods to find the estimators of the risk function and some of its indicators for the two-parameter truncated Cauchy distribution in the case of the availability of preliminary information on the parameters in the form of an initial probability function and in the absence of information based on the Jeffrey method for each of the shape parameter and the measurement parameter using six Bayesian methods, which are both the non-informative standard Bayes estimator method, the information standard Bayes estimator method, and the( Bayesian expectation method. Loss Function) is not symmetrical, and because of the difficulty of the calculations for calculating the estimators of the risk function by using the impregnable fuzzy Bayesian methods, the numerical analysis method was used .
The simulation method was employed using the (Monte-Carlo) method to generate random data for a sample consisting of six different sizes (15-25-35-50-75-100) following the truncated Cauchy distribution with two parameters, as well as default values ​​for the two distribution parameters were determined by ten models with the aim of Obtaining new, high-accuracy estimators that carry the required characteristics in the ideal estimator that is relied upon in the estimation process, and based on the simulation results and using the statistical mean squared error (MSE) criterion as a statistical criterion for comparison. For medium and large sample sizes to estimate the risk function over other estimation methods .
The study was conducted on a real sample of (100) observations representing ECG failure times in months, which were obtained from the records of the administration of Al-Hussein Teaching Hospital in the holy city of Karbala. That the estimation methods used in the applied side give appropriate and accurate estimates for the study data and agree with what was reached in the experimental side .