An Application of Generalized Entropy Optimization Methods in Survival Data Analysis

Shamilov, Aladdin; Kalathilparmbil, Cigdem; Özdemir, Sevda

doi:10.4236/jmp.2017.83024

Cited by 2 publications

(4 citation statements)

References 13 publications

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“…It must be noted that calculating Lagrange multipliers can be fulfilled by starting from arbitrary initial point for Newton's approximations of constructed auxiliary equation [12].…”

Section: The Existence Of Solutions Ofmentioning

confidence: 99%

“…[19][20][21] The investigation of these problems leads to GEOP are stated and studied. 12 And also, same applications are given. [22][23] Our study consists of following sections.…”

mentioning

confidence: 99%

“…10 In the mentioned papers the approach to obtain MinMaxEnt and MaxMinxEnt distributions can be formulated as a generalization of Entropy Optimization Methods. EOM have important applications, especially in statistics, physics, engineering, economy, survival data analysis [11][12][13] , fuzzy logic, wind energy and so on. 14,15 Moreover, there are many studies about the application of mentioned methods in the literature when known statistical distributions do not conform to statistical data, but the entropy optimization distributions conform well.…”

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confidence: 99%

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On Several New Generalized Entropy Optimization Methods

Shamilov¹,

Ince²

2016

Turkiye Klinikleri J Biostat

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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 Min MaxEnt , Max MaxEnt; GEOD3 in the form of Min MinxEnt , Max MinxEnt, where is the Jaynes optimization measure, is Kullback-Leibler optimization measure. It should be noted that formulation of GEOP1 uses only one optimization measure ( or ), however each of formulations of GEOP2, GEOP3 uses two measures , 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 , in dependency of requirements of experimental situation.

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“…It must be noted that calculating Lagrange multipliers can be fulfilled by starting from arbitrary initial point for Newton's approximations of constructed auxiliary equation [12].…”

Section: The Existence Of Solutions Ofmentioning

confidence: 99%

“…[19][20][21] The investigation of these problems leads to GEOP are stated and studied. 12 And also, same applications are given. [22][23] Our study consists of following sections.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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On Several New Generalized Entropy Optimization Methods

Shamilov¹,

Ince²

2016

Turkiye Klinikleri J Biostat

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“…In Section 6, the maximum fuzzy entropy value is achieved. In Section 7, new Generalized Maximum Fuzzy Entropy Problems (MinMax(F)Ent) m , (MaxMax(F)Ent) m and methods of solving these problems are developed [18][19][20]. In Section 8, it is given an application about GMax(F)EntM.…”

Section: Introductionmentioning

confidence: 99%

Bulanık Üyelik Fonksiyonunun Yaklaşımı İçin Bir Yeni Metot ve Uygulama

Ince¹,

Shamilov²

2017

Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler

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In the present study we have formulated a new Maximum Fuzzy Entropy Problem (Max(F)EntP) for fuzzy membership function and proposed sufficient conditions for existence of its solution. Mentioned problem consists of approximation fuzzy membership function by maximizing Maximum Fuzzy Entropy (Max(F)Ent) measure with respect to membership functions with finite number of the fuzzy values subject to constraints generated by given moment functions. The existence of solution of mentioned problem is proved by virtue of convexity property of Max(F)Ent measure, the implicit function theorem and Lagrange multipliers method. Moreover, by using MATLAB programme one application of suggested method on fuzzy data analysis is given.

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An Application of Generalized Entropy Optimization Methods in Survival Data Analysis

Abstract: In this paper, survival data analysis is realized by applying Generalized Entropy Optimization Methods (GEOM

Cited by 2 publications

References 13 publications

On Several New Generalized Entropy Optimization Methods

On Several New Generalized Entropy Optimization Methods

Bulanık Üyelik Fonksiyonunun Yaklaşımı İçin Bir Yeni Metot ve Uygulama

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