Estimating the Hazard Function of a Transformed Kappa Distribution with Practical Application

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

Manal mousa abd al-ema

Supervised By

Prof.Dr Mahdi Wahab Neama Naser Allah

we discuss the three-parameter kappa distribution and work on a new study of the distribution through the quadratic transformation map Thus, the kappa distribution becomes a transformer with four parameters and is characterized by flexibility and accuracy over other distributions. The properties of the distribution have been studied and extracted, and the distribution has been applied to five of the traditional estimation methods. This is the method used in the thesis (Maximum Likelihood Method, Cramer-Von Mises Minimum, Anderson- Darling, Right–TailAnderson- Darling, Left-Tail  Anderson- Darling). In order to find the best method among the estimation methods, the Monte-Carlo simulation method was used. Using the (Mathematica 12.2) program, eight models for different sample sizes (small, medium, large) were used and different values were selected for the distribution parameters, and the aim of it is to study the behavior of the measures using mean squares of error (MSE), medium and large. The distribution was applied to real data for heart patients. The sample size was 104 observations, representing the patient’s survival times until death, using good-match criteria. The preference of the transferred distribution was proven compared to the distribution before transfer and other distributions under study. Also, the estimation of the risk function was applied using the best methods that were reached on the experimental side (the method of greatest possibility) and that the average survival times is (0.470068), meaning that the probability of survival of the patient with heart disease is approximately 50%.