Analysis of the Survival function when the coefficient  Hazard proportional with time (Applied Study)

Thesis Submitted to the College of Administration and Economic- University of Karbala in partial fulfillment of the Requirements for the Degree of master of Science in statistics

By
 Atheer Abd Alzahra
Under supervision of
Prof . Dr . Abdul Hussain H. H. al-Tai

ABSTRACT

It is known that the study and analysis of survival functions and a ccurate

Therefore ,it  must search for good method of estimation with small Mean Square Error (MSE) or any other Test statisticas  possible.

Hence, this thesis consist of studying and analyzing the survival functions and there indicators by using parametric and nonparametric method for Hazard function which is proportional with the time. Also, the appropriate distribution was determined by finding a relationship between

The Hazard  coefficient  and Time.

The results showed that the appropriate distribution Weibull distribution.

Therefore ,we forus on this on this distribution to analysis the survival function as a parametric method .

Mean while , in the nonparametric method we got the survival function by applying the cumulative function which is considered as a complement for the survival , Also the hazard coefficient was used to determine the survival function .on other hand , we use asset of data from mergan educational hospital in Babil govern on ate which consist number of wounded who were hospitalized due to one of the terrorist bombings

Then we count the number of  survival and the number of died with in a period of 288 hours . The results showed that the estimator methods (cumulative function  and hazard coefficient  ) are same in the small large sample and there value is equal or less than 25.later we use the simulation study to be sure form the applied results. The simulation results showed that the sharinkge method for small samples is the best because they achieved less MSE and maximum likelihood is the best for the large sample because they achieved less MSE, meanwhile the white method is the less efficiency in estimation .