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- Title
On Several New Generalized Entropy Optimization Methods.
- Authors
SHAMILOV, Aladdin; İNCE, Nihal
- Abstract
Objective: In this study we have suggested new Generalized Entropy Optimization Methods (GEOM) for solving Entropy Optimization Problems (EOP) consisting of optimizing a given entropy optimization measure subject to constraints generated by given moment vector functions. These problems acquire in different scientific fields as statistics, information theory, biostatistics especially in survival data analysis and etc. Material and Methods: Mentioned problems in the form of GEOP2,GEOP3 based on GEOP1 have Generalized Entropy Optimization Distributions: GEOD2 in the form of MinD MaxEnt ,MaxD MaxEnt; GEOD3 in the form of MinH MinxEnt ,MaxH MinxEnt, where H is the Jaynes optimization measure, D is Kullback-Leibler optimization measure. It should be noted that formulation of GEOP1 uses only one optimization measure (H or D), however each of formulations of GEOP2, GEOP3 uses two measures H, D together. Results: GEOP 1,2,3 are conditional optimization problems which can be solved by Lagrange multipliers method. It must be noted that calculating Lagrange multipliers can be fulfilled by starting from arbitrary initial point for Newton approximations of constructed auxiliary equation. Conclusion: There are situations, for example in survival data analysis, when both MaxEnt and MinxEnt distributions are accepted to given statistical data (or distribution) in the sense of same goodness of fit test. For this reason, developed our methods to obtain distributions are fundamental in statistical analysis. Analogous generalized problems can be also considered by the virtue of other measures different from H , D in dependency of requirements of experimental situation.
- Publication
Turkiye Klinikleri Journal of Biostatistics, 2016, Vol 8, Issue 2, p110
- ISSN
1308-7894
- Publication type
Academic Journal
- DOI
10.5336/biostatic.2016-52369