استعمال الطرائق البيزية الضبابية لتقدير معلمات التوزيع Kibble-Bivariate Gamma مع التطبيق العملي

Rp-Use of Fuzy Bayesian Methods to Estimate Parameters of the Kibble-Bivariate Gamma Distribution .pdf

: In many applied cases, we encounter data that may be interrelated with each other, as in clinical trials that involve survival analysis for interrelated failure times. Therefore, such data must be dealt with according to a probabilistic model that works to model such interrelated phenomena, and because there are many of these phenomena that suffer from The inaccuracy in its measurements, therefore, will have the characteristic of fuzziness and is expressed in fuzzy numbers. To estimate the parameters of the probability distribution that represents these interrelated data in light of the fuzzy environment, it is necessary to generalize the concept of fuzziness and move from the usual (traditional) estimation methods to those specialized in fuzziness. To obtain accurate and accurate estimates of the phenomena under study.
This thesis came with the aim of estimating the parameters of Kibble’s Bivariate gamma distribution using the standard Bayesian method of estimation under the measurements of two fuzzy interconnected random variables under the quadratic loss function and a precautionary loss function. The thesis dealt with two aspects, the first is the experimental aspect in which Monte-Carlo simulation experiments were used to test the preference of the two estimation methods used in this thesis. It was concluded through simulation experiments that the Bayes method at a precautionary loss function recorded the highest percentage of preference (79%) compared to the Bayes method at a precautionary loss function. Squared loss with a priority rate of (21%). And at the cutoff (Alpha-cut = 0.3), the Bayesian method with a squared loss function was the best with a priority rate of (60%). While the Bayes method recorded at (Alpha-cut = 0.5, 0.8) a percentage of (20%) for each cut-off factor, and this indicates that the greater the cut-off in the fuzzy group, the lower the preference for the squared loss function of the Bayesian estimator. The Bayes method recorded at a precautionary loss function and at (Alpha-cut = 0.3) a preference rate of (26%), while it recorded at (Alpha-cut = 0.5, 0.8) a preference rate of (37%) for each cut-off parameter, and this indicates It is a Bayesian method when the precautionary loss function is the best as the cutoff increases in the fuzzy set. On the applied side, the Bayesian method was used under a precautionary loss function in light of data representing two random variables, namely (X) the amount of rain falling on Iraq, measured in milliliters, and (Y) the intensity of rain falling in mm/hour in all governorates of Iraq, with a rate of (150). Reading Each reading expresses the amount of rain and the intensity of rain within (24) hours, as the variables were tested in terms of their correlation and suitability to Kibble’s Bivariate gamma distribution. On the applied side, the superiority of the Bayes method was reached under the precautionary loss function by using real data at the cut-off coefficient (Alpfa-Cut = 0.5), as it was the lowest mean square error is (0.001062). The greater the cutoff in the fuzzy set, the less elements that have less or equal cutoffs, and thus increase the accuracy of the estimation method. The estimated parameters at the real data are closer to the default parameters (α = 4.5, β = 2, ρ = 0.9), which gave the best results in the simulation experiments