scholarly journals Sample Dependence in the Maximum Entropy Solution to the Generalized Moment Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Henryk Gzyl
Keyword(s):  
Probability Density ◽  
Maximum Entropy ◽  
Moment Problem ◽  
Entropy Solution ◽  
Random Variable ◽  
Actual Practice ◽  
Expected Values ◽  
Generalized Moment Problem ◽  
Generalized Moment

The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists in determining the probability density of a random variableXfrom the knowledge of the expected values of a few functions of the variable. In actual practice, such expected values are determined from empirical samples, leaving open the question of the dependence of the solution upon the sample. It is the purpose of this note to take a few steps towards the analysis of such dependence.

Maximum entropy in the generalized moment problem

1998 ◽  
Vol 39 (12) ◽  
pp. 6706-6714 ◽  
Author(s):  
M. Frontini ◽  
A. Tagliani
Keyword(s):  
Maximum Entropy ◽  
Moment Problem ◽  
Generalized Moment Problem ◽  
Generalized Moment

A generalized moment problem

1962 ◽  
Vol 146 (4) ◽  
pp. 326-330 ◽  
Author(s):  
Helmut H. Schaefer
Keyword(s):  
Moment Problem ◽  
Generalized Moment Problem ◽  
Generalized Moment

scholarly journals Numerical Algorithms for Estimating Probability Density Function Based on the Maximum Entropy Principle and Fup Basis Functions

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1559
Author(s):  
Nives Brajčić Kurbaša ◽  
Blaž Gotovac ◽  
Vedrana Kozulić ◽  
Hrvoje Gotovac
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Moment Problem ◽  
Statistical Power ◽  
Maximum Entropy Principle ◽  
Basis Functions ◽  
Approximation Properties ◽  
Hybrid Strategy

Estimation of the probability density function from the statistical power moments presents a challenging nonlinear numerical problem posed by unbalanced nonlinearities, numerical instability and a lack of convergence, especially for larger numbers of moments. Despite many numerical improvements over the past two decades, the classical moment problem of maximum entropy (MaxEnt) is still a very demanding numerical and statistical task. Among others, it was presented how Fup basis functions with compact support can significantly improve the convergence properties of the mentioned nonlinear algorithm, but still, there is a lot of obstacles to an efficient pdf solution in different applied examples. Therefore, besides the mentioned classical nonlinear Algorithm 1, in this paper, we present a linear approximation of the MaxEnt moment problem as Algorithm 2 using exponential Fup basis functions. Algorithm 2 solves the linear problem, satisfying only the proposed moments, using an optimal exponential tension parameter that maximizes Shannon entropy. Algorithm 2 is very efficient for larger numbers of moments and especially for skewed pdfs. Since both Algorithms have pros and cons, a hybrid strategy is proposed to combine their best approximation properties.

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