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Updated: Oct 30, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Entropy Optimization, Maxwell-Boltzmann, and Rayleigh Distributions.

Nicy Sebastian1, Arak M Mathai2, Hans J Haubold3

  • 1Department of Statistics, St. Thomas College, Thrissur, Kerala 680001, India.

Entropy (Basel, Switzerland)
|July 2, 2021
PubMed
Summary
This summary is machine-generated.

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Optimizing a novel entropy measure allows derivation of various real and complex univariate, multivariate, and matrix-variate distributions. This entropy-based method provides a unified approach for statistical modeling.

Area of Science:

  • Statistical Physics
  • Information Theory
  • Probability Theory

Background:

  • Entropy optimization is a key method for deriving probability distributions across scientific disciplines.
  • Existing methods may not cover the full spectrum of univariate, multivariate, and matrix-variate distributions in both real and complex domains.

Purpose of the Study:

  • To demonstrate the derivation of diverse statistical distributions using a specific entropy measure.
  • To extend the application of entropy optimization to complex domains and matrix-variate statistics.

Main Methods:

  • Optimization of a novel entropy measure under relevant constraints.
  • Derivation of probability density functions for various distribution types.

Main Results:

Keywords:
complex Maxwell–Boltzmann and Rayleigh densitiesellipsoid of concentrationgeneralized entropygeneralized gammamatrix-variate pathway modelsmultivariate and matrix-variate densitiesoptimization of entropytype-1, type-2 beta densities

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  • Successfully derived univariate, multivariate, and matrix-variate distributions in real and complex domains.
  • Included are Maxwell-Boltzmann, Rayleigh, Student-t, Cauchy, and Beta/Gamma distributions and their generalizations.

Conclusions:

  • The proposed entropy measure offers a powerful and unified framework for deriving a wide range of statistical distributions.
  • This approach has broad applicability in physics, engineering, and statistics, particularly for complex and matrix-variate data.