ESTIMATION OF PROBABILITY DENSITY FUNCTION AND INTENSITY FUNCTION OF THE SURVIVAL OF STOMACH CANCER PATIENTS USING REAL POLYNOMIALS
Keywords:
nonparametric estimation, polynomial density estimator, intensity estimation, stomach cancer.DOI:
https://doi.org/10.17654/0973514322010Abstract
Various parametric and nonparametric approaches are available in the literature for estimating the probability density function and intensity function of the censored data. A retrospective study was carried out on the stomach cancer patients who registered in a tertiary cancer centre during the years 2010 and 2011. Their treatment and demographic characteristics have been studied. The density function and intensity function were estimated using a real polynomial that Rudin used to prove Stone-Weierstrass theorem.
Received: November 28, 2021
Revised: January 24, 2022
Accepted: January 29, 2022
References
O. Aalen, Nonparametric inference for a family of counting processes, Ann. Statist. 6(4) (1978), 701-726.
P. Anilkumar et al., Density estimation using polynomial for complete and right censored samples, Far East Journal of Theoretical Statistics 55(1) (2019), 1-21.
J. Marron and W. Padgett, Asymptotically optimal bandwidth selection for kernel density estimators from randomly right-censored samples, Ann. Statist. 15 (1987), 1520-1535.
E. Parzen, On estimation of a probability density function and mode, Ann. Math. Statist. 33 (1962), 1065-1076.
H. Ramlau-Hansen, Smoothing counting process intensities by means of kernel functions, Ann. Statist. 11(1983), 453-466.
K. Ratheesan and P. Anilkumar, Smoothing intensities of counting processes by using polynomial, JP Journal of Biostatistics 18(2) (2021), 209-230.
M. Rosenblatt et al., Remarks on some nonparametric estimates of a density function, Ann. Math. Statist. 27(3) (1956), 832-837.
W. Rudin et al., Principles of Mathematical Analysis, Vol. 3, McGraw-Hill, New York, 1964.
B. W. Silverman, Density Estimation for Statistics and Data Analysis, Vol. 26, CRC Press, 1986.
L. Devroye and L. Gyorfi, Nonparametric Density Estimation: The L1 View, John Wiley and Sons, New York, 1985.
M. P. Wand and M. C. Jones, Kernel Smoothing, Chapman & Hall, London, 1995.
W. Nelson, Theory and application of hazard plotting for censored failure data, Technometrics 14 (1972), 945-966.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Pushpa Publishing House, Prayagraj, India

This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Puspha Publishing House for more info or permissions.
Journal Impact Factor: 


Google h-index: 10