Estimation Survival function Distribution Odd Chen Frechet

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala University as Partial fulfillment of the Requirements for the Degree of Master of Science in Statistics

Presented by researcher

Supervised By

Shahad Emad Abdel Rasool 

Under supervision

Sada Fayed Mohammed

The study seeks to use the theory of compound distributions in constructing a new proposed probability distribution known as (Odd Chen Distribution) with four parameters (α, β, γ, θ), as some of its properties were studied, its parameters were estimated and survival function estimators were calculated using four estimation methods (Maximum Likelihood Method (MLE), the Cramer von Masse method (CVM), the method of weighted least squares (WLS) and the method of partial estimators (Per). MATLAB to conduct several experiments with different sample sizes (30, 50, 75, 100, 150), small, medium and large, and by means of the statistical mean square error (MSE). Small, medium and large, and the preference of the weighted least squares method for small sample sizes. The distribution was applied using the method whose preference appeared on the experimental side on real data with a rate of (110) observations in weeks representing the survival times for people with kidney failure until death, and by means of good fit tests, its preference in representing and describing these data was proven compared to the distribution (Odd Chen Distribution). Also, the survival function was estimated for real data using the Cramer von Mises method, which showed its preference in the experimental side, and we found that the average survival time for people with kidney failure until death was (3.233), and that the average value of death for a person with kidney failure was (17). almost a week.

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala University as Partial fulfillment of the Requirements for the Degree of Master of Science in Statistics

Presented by researcher

Supervised By

Shahad Emad Abdel Rasool 

Under supervision

Sada Fayed Mohammed

The study seeks to use the theory of compound distributions in constructing a new proposed probability distribution known as (Odd Chen Distribution) with four parameters (α, β, γ, θ), as some of its properties were studied, its parameters were estimated and survival function estimators were calculated using four estimation methods (Maximum Likelihood Method (MLE), the Cramer von Masse method (CVM), the method of weighted least squares (WLS) and the method of partial estimators (Per). MATLAB to conduct several experiments with different sample sizes (30, 50, 75, 100, 150), small, medium and large, and by means of the statistical mean square error (MSE). Small, medium and large, and the preference of the weighted least squares method for small sample sizes. The distribution was applied using the method whose preference appeared on the experimental side on real data with a rate of (110) observations in weeks representing the survival times for people with kidney failure until death, and by means of good fit tests, its preference in representing and describing these data was proven compared to the distribution (Odd Chen Distribution). Also, the survival function was estimated for real data using the Cramer von Mises method, which showed its preference in the experimental side, and we found that the average survival time for people with kidney failure until death was (3.233), and that the average value of death for a person with kidney failure was (17). almost a week.