Abstract
In this major paper, a nonparametric estimator of the joint cumulative distribution function using Poisson probability under right censoring was proposed and discussed. In particular, the joint cumulative distribution of two non-negative random variables X and Y was of interest in this work, where X was assumed to be complete, while Y was subjected to right censoring. The asymptotic properties of the proposed estimator (called hereafter Poisson polynomial estimator) were established, including independent and identically distributed representation, expectation and variance, and asymptotic normality.
Furthermore, two real datasets were analyzed to assess the Poisson polynomial estimator: Loss-ALAE joint distribution estimation and age’s impact on survival in patients with colon cancer. Also, the Stute empirical estimator and empirical Bernstein estimator were introduced as a comparison. Evidence reveals that the Poisson estimator gives a more precise value along with the best effect on smoothness among all three estimators and provides an alternative solution for future simulation and prediction. However, more calculations are required to obtain a precise solution with an acceptable error as the Poisson probability takes values from zero to infinity.
Primary Advisor
Dr. Mohamed Belalia
Program Reader
Dr. Myron Hlynka
Degree Name
Master of Science
Department
Mathematics and Statistics
Document Type
Major Research Paper
Convocation Year
2022