A Comparison of Survivor Rate Estimates for Some Probability Distribution Models Using Least-Squares Method in Conjunction with Simplex and Quasi-Newton Optimization Methods

Abstract

In this paper, we find survival rate estimates, parameter estimates, variance covariance for some probability distribution models like, Exponential, Inverse Gaussian, Gompertz, Gumbels and Weibull distributions using least-squares estimation method. We found these estimates for the case when partial derivatives were not available and for the case when partial derivatives were available. The first case when partial derivatives were not available, we used the simplex optimization (Nelder and Meads ([6],[7]) and Hooke and Jeeves ([4],[5])) methods and the case when first partial derivatives were available we applied the Quasi – Newton optimization (Davidon-Fletcher-Powel (DFP) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) methods. The medical data sets of 21 Leukemia cancer patients with time span of 35 weeks ([3]) were used.