طريقة جديدة بيزية ضبابية حصينة عامة للتوزيعات الإحتمالية

Rp-A new general robust fuzzy Bayesian method for probability distributions.pdf

Abstract:
In many situations of daily life, and upon initiating with operations of statistical analysis, we encounter data that suffers from inaccuracies in its measurement, either due to errors of observation or measurement, or the lack of appropriate conditions for collecting such data, such as failure times of machines, equipment, and electrical devices, medical, engineering and economic data. These data are often accompanied by values that may be far from the original data format and which constitute data with a heavier tail. When estimating these phenomena that suffer from inaccuracy in their measurement (fuzziness) in addition to the presence of outlier values in them using the usual estimation methods, this leads to misleading, inaccurate and unrepresentative estimates of the reality of the phenomenon being studied. Therefore, it is necessary to find appropriate and robust methods of estimation under these circumstances to ensure the accuracy of the obtained estimations. In this thesis, a method is proposed to transform any traditional probability distribution into a fuzzy probability distribution using the 𝛼-cut set principle, by finding the fuzzy cumulative distributon function F ̃(t ̃_(A^((α)) ) ) at any value of the set of segments t ̃_(A^((α)) ) and then derive this fuzzy cumulative to find the fuzzy probability function f ̃(t ̃) And then to find a Bayesian method that has robust by proposing that for each of the parameters to be estimated at each item of the sample vector ti drawn from a probability distribution φ(t_i  θ_i ) there is an initial information represented by an initial distribution π(θ_i  ▁ϑ) for the parameter θ_i with the meta parameter(s) ▁ϑ by integrating the proposed fuzzy probability distribution with the proposed robust Bayesian method, a new general robust Bayesian fuzzy method was obtained for the probability distributions. By using Monte-Carlo simulation experiments, the proposed method was tested and compared with the normal Bayesian method by generating a crisp sample with a size of (100) observations, and then using five cut-off values (α-cut = 0.2, 0.4, 0.5, 0.7, 0.9), and the data were polluted with an oulites One, two and three values, and then the fuzzy groups that were used to find the estimators of Bayes were obtained. This method was applied to three probability distributions, namely, the Exponential, Weibull, and Standard Kumaraswamy distribution. It was concluded that the proposed method is effective in estimating the parameters of the probability distribution more accurately than the normal Bayesian method when the data contains outliers. The proposed method was also applied to real data representing failure times of the heart stent (heart catheter stent), which represents the time per month from the beginning of the cardiac stent installation until the stent stopped working (failure) for (100) patients for whom cardiac catheterization was performed, which was obtained from Shahid Al-Mihrab Center for Cardiac Catheterization and Surgery affiliated to Marjan General Teaching Hospital – Babylon Health Department during the year (2021) and it was concluded that the method is effective and appropriate in estimating the parameters of the real data distribution.