On the Distribution of the Information Density of Gaussian Random Vectors: Explicit Formulas and Tight Approximations
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
Based on the canonical correlation analysis, we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as a general formula to calculate the central moments. Using the general results, we give closed-form expressions of the PDF and CDF and explicit formulas of the central moments for important special cases. Furthermore, we derive recurrence formulas and tight approximations of the general series representations, which allow efficient numerical cal-culations with an arbitrarily high accuracy as demonstrated with an implementation in PYTHON publicly available on GITLAB. Finally, we discuss the (in)validity of Gaussian approximations of the information density.
Details
Original language | English |
---|---|
Article number | 924 |
Number of pages | 29 |
Journal | Entropy |
Volume | 24 |
Issue number | 7 |
Publication status | Published - Jul 2022 |
Peer-reviewed | Yes |
External IDs
Scopus | 85133729426 |
---|---|
PubMed | 35885147 |
Mendeley | 8c63e9f1-7be9-3e4c-91a0-aeafff5ea215 |
unpaywall | 10.3390/e24070924 |
Keywords
ASJC Scopus subject areas
Keywords
- Gaussian random vector, canonical correlation analysis, central moments, cumulative distribution function, information density, information spectrum, probability density function