Open AccessContinuous MaxEnt Distributions in Mathematica: a “Parameter-Free” Approach
Author(s) -
Barrie Stokes,
Paul M. Goggans,
Chun-Yong Chan
Publication year - 2009
Publication title -
aip conference proceedings
Language(s) - English
Resource type - Conference proceedings
SCImago Journal Rank - 0.177
H-Index - 75
eISSN - 1551-7616
pISSN - 0094-243X
DOI - 10.1063/1.3275626
Subject(s) - lagrange multiplier , interpolation (computer graphics) , probability density function , multiplier (economics) , mathematics , lagrange polynomial , function (biology) , differential equation , partial differential equation , computer science , domain (mathematical analysis) , numerical integration , mathematical optimization , algorithm , mathematical analysis , statistics , polynomial , animation , computer graphics (images) , evolutionary biology , biology , economics , macroeconomics
Mathematica is used to develops a method of obtaining continuous MaxEnt distributions using the Lagrange Multiplier method that works directly in the discrete case. The continuous PDF (probability density function) is described by list of coordinates of the form {{abs₁, ord₁}, {abs₂, ord₂}, ... , {absn, ordn}}, where the abscissae absᵢ are specified numerically so as to define the domain of the PDF, and the ordinates ordᵢ are initially general symbolic variables that are assigned numeric values via the procedure to be described. In all the applications given here, n = 51. A set of Lagrange Multiplier equations is solved for the ordi, making use of the fact that the Mathematica function Interpolation[], which constructs interpolationFunction objects normally used for numeric data and for describing numerical solutions to differential equations, can operate on "semi-symbolic" data
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