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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.

In this study, a new method to obtain approximate probability density function (pdf) of random variable of solution of stochastic differential equations (SDEs) by using generalized entropy optimization methods (GEOM) is developed. By starting given statistical data and Euler–Maruyama (EM) method approximating SDE are constructed several trajectories of SDEs. The constructed trajectories allow to obtain random variable according to the fixed time. An application of the newly developed method includes SDE model fitting on weekly closing prices of Honda Motor Company stock data between 02 July 2018 and 25 March 2019.

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

This study is connected with new Generalized Maximum Fuzzy Entropy Methods (GMax(F)EntM) in the form of MinMax(F)EntM and MaxMax(F)EntM belonging to us. These methods are based on primary maximizing Max(F)Ent measure for fixed moment vector function in order to obtain the special functional with maximum values of Max(F)Ent measure and secondary optimization of mentioned functional with respect to moment vector functions. Distributions, in other words sets of successive values of estimated membership function closest to (furthest from) the given membership function in the sense of Max(F)Ent measure, obtained by mentioned methods are defined as (MinMax(F)Ent) m which is closest to a given membership function and (MaxMax(F)Ent) m which is furthest from a given membership function. The aim of this study consists of applying MinMax(F)EntM and MaxMax(F)EntM on given wind speed data. Obtained results are realized by using MATLAB programme. The performances of distributions (MinMax(F)Ent) m and (MaxMax(F)Ent) m generated by using Generalized Maximum Fuzzy Entropy Methods are established by Chi-Square, Root Mean Square Error criterias and Max(F)Ent measure.