Dr. Khizar Hayat Khan - Academia.edu (original) (raw)
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Papers by Dr. Khizar Hayat Khan
Advances in Dynamical Systems and Applications, 2021
In this paper, we find survival rate estimates, parameter estimates, variance covariance for some... more 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.
Journal of Applied Mathematics and Computation, 2018
We find Survival rate estimates; parameter estimates for the inverse Gaussian distribution model ... more We find Survival rate estimates; parameter estimates for the inverse Gaussian distribution model using least-squares estimation method. We found these estimates for the case when partial derivatives were available and for the case when partial derivatives were not available. The simplex optimization (Nelder and Mead, and Hooke and Jeeves) methods were used for the case when first partial derivatives were not available and the Quasi-Newton optimization (Davidon-Fletcher-Powel (DFP) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) methods were applied for the case when first partial derivatives were available. The medical data sets of 21 Leukemia cancer patients with time span of 35 weeks were used.
Advances in Dynamical Systems and Applications, 2021
In this paper, we find survival rate estimates, parameter estimates, variance covariance for some... more 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.
Journal of Applied Mathematics and Computation, 2018
We find Survival rate estimates; parameter estimates for the inverse Gaussian distribution model ... more We find Survival rate estimates; parameter estimates for the inverse Gaussian distribution model using least-squares estimation method. We found these estimates for the case when partial derivatives were available and for the case when partial derivatives were not available. The simplex optimization (Nelder and Mead, and Hooke and Jeeves) methods were used for the case when first partial derivatives were not available and the Quasi-Newton optimization (Davidon-Fletcher-Powel (DFP) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) methods were applied for the case when first partial derivatives were available. The medical data sets of 21 Leukemia cancer patients with time span of 35 weeks were used.