Bayesian Estimation of Parameters of a Consul Kumaraswamy distribution under a Squared loos function and a General entropy loos function 

(An Empirical Study )

A thesis

Submitted to the council of the college of administration and Economic\ University of Karbala, as Partial fulfillment of the Requirements for the Degree of Master of Science in Statistic

Written by

Noor Amer Harb AL-Bazuny

Supervised byProf. Dr. Awad Kazem Shaalan AL-Khalidy

The study seeks to use the Bayesian methods represented by the Standard Informative Bayesian method and the Expected Bayesian method to find the capabilities and survival function of the Consul kumaraswamy dist. (CKSD) with three parameters (m, α, β) within a symmetrical loss function called the squared error loss function, and an asymmetrical one called a general entropy loss function.
In order to simplify and solve the equations resulting from the above estimation methods, the approximate method proposed by the researcher Lindley, which is called the Lindley Approximation method, and another method called the Jeffry method was used, where the two methods were compared to find out which one is more accurate in solving non-linear equations that cannot be solved Using numerical analysis methods

For the purpose of comparing the Bayesian estimation methods used to find the estimators and survival function of the Consul Kumaraswamy dist., the Monte Carlo simulation method was employed using the MATLAB program by conducting several experiments with different small sample sizes (10, 20). ), medium (30,40) and large (50), and by means of the statistical criterion mean squares of integral error IMSE, the results showed the preference of the Bayesian prediction method in light of the general entropy loss function when Lindley approximation over the rest of the estimation methods. In addition to the superiority of the Lindley approximation to the Jeffrey approximation with an advantage of 36% and for all simulation experiments and to apply the distribution of the Consul Kumaraswamy on the ground, a sample of 50 individuals was drawn representing the duration of stay of patients with ischemic heart disease in Al-Hussein Teaching Hospital in the Holy Karbala Governorate Through the good-matching test, it was proved that the distribution of Consul Kumaraswamy is preferable in representing and describing these data compared to the distribution of Consul Kumaraswamy. The survival function in the real data was also estimated using the estimation methods that were applied in the experimental side, where we note that the estimated parameters of the real data for the distribution of Consul Komarswami are more close to the default parameters on the experimental side, that is, the Bayes prediction estimator method under the general entropy loss function is better than the rest The methods when applied to the real data, and the estimated values ​​of the survival function according to Bayesian prediction method under the general entropy loss function are better than the rest of Bayesian methods as they are more close to the real survival function.

Bayesian Estimation of Parameters of a Consul Kumaraswamy distribution under a Squared loos function and a General entropy loos function 

(An Empirical Study )

A thesis

Submitted to the council of the college of administration and Economic\ University of Karbala, as Partial fulfillment of the Requirements for the Degree of Master of Science in Statistic

Written by

Noor Amer Harb AL-Bazuny

Supervised byProf. Dr. Awad Kazem Shaalan AL-Khalidy

The study seeks to use the Bayesian methods represented by the Standard Informative Bayesian method and the Expected Bayesian method to find the capabilities and survival function of the Consul kumaraswamy dist. (CKSD) with three parameters (m, α, β) within a symmetrical loss function called the squared error loss function, and an asymmetrical one called a general entropy loss function.
In order to simplify and solve the equations resulting from the above estimation methods, the approximate method proposed by the researcher Lindley, which is called the Lindley Approximation method, and another method called the Jeffry method was used, where the two methods were compared to find out which one is more accurate in solving non-linear equations that cannot be solved Using numerical analysis methods

For the purpose of comparing the Bayesian estimation methods used to find the estimators and survival function of the Consul Kumaraswamy dist., the Monte Carlo simulation method was employed using the MATLAB program by conducting several experiments with different small sample sizes (10, 20). ), medium (30,40) and large (50), and by means of the statistical criterion mean squares of integral error IMSE, the results showed the preference of the Bayesian prediction method in light of the general entropy loss function when Lindley approximation over the rest of the estimation methods. In addition to the superiority of the Lindley approximation to the Jeffrey approximation with an advantage of 36% and for all simulation experiments and to apply the distribution of the Consul Kumaraswamy on the ground, a sample of 50 individuals was drawn representing the duration of stay of patients with ischemic heart disease in Al-Hussein Teaching Hospital in the Holy Karbala Governorate Through the good-matching test, it was proved that the distribution of Consul Kumaraswamy is preferable in representing and describing these data compared to the distribution of Consul Kumaraswamy. The survival function in the real data was also estimated using the estimation methods that were applied in the experimental side, where we note that the estimated parameters of the real data for the distribution of Consul Komarswami are more close to the default parameters on the experimental side, that is, the Bayes prediction estimator method under the general entropy loss function is better than the rest The methods when applied to the real data, and the estimated values ​​of the survival function according to Bayesian prediction method under the general entropy loss function are better than the rest of Bayesian methods as they are more close to the real survival function.