Estimation of the survival function for a Compound probability distribution (Weibull – Rayleigh) 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
By Ahmed Ajel Mjely
Supervised By
Assistant Prof. Dr.Shrooq Abd-ALRida Saeed
Abstract:
Computed probability distributions are important distributions especially in recent decades because they are important in the process of data modeling because they are flexible and are compatible with most data and the complex distributions result from the installation of two or more distributions, In this study, we used a three-dimensional composite probability distribution (Weibull – Rayleigh). We studied some mathematical characteristics of this distribution Such as aggregate function, probabilistic density function, survival function and risk function as well as estimation of new composite distribution parameters and survival function Using three methods of estimation (Maximum Likelihood Method, Least Squares Method, Weighted Least Squares Method) The three methods were compared using MSE using the simulation method. The experiment was carried out using sample sizes (small, medium, large) The experiment was repeated 1000 times to achieve more homogeneity. Through the simulation results, the advantage of the WLS method was in estimating the survival function of the composite distribution.
On the practical side, a random sample of data (47 persons) was performed on the number of deaths of breast cancer patients in Dhi Qar governorate for the period from 1/1/2013 to 6/10/2016, where the period of their survival, This sample of data was applied to the composite distribution as well as Wibble distribution and Riley distribution. To better represent the data, a number of differentiation criteria were used to compare distributions Through the results of the criteria (AIC, BIC, AICC) shows that the composite distribution is better than the other distributions in the representation of the data studied, The survival function was then estimated using the best method reached by the researcher on the experimental side.
