Determination of System Dimensionality from Observing Near-Normal Distributions
Joint Authors
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-08-31
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
This paper identifies a previously undiscovered behavior of uniformly distributed data points or vectors in high dimensional ellipsoidal models.
Such models give near normal distributions for each of its dimensions.
Converse of this may also be true; that is, for a normal-like distribution of an observed variable, it is possible that the distribution is a result of uniform distribution of data points in a high dimensional ellipsoidal model, to which the observed variable belongs.
Given the currently held notion of normal distributions, this new behavior raises many interesting questions.
This paper also attempts to answer some of those questions.
We cover both volume based (filled) and surface based (shell) ellipsoidal models.
The phenomenon is demonstrated using statistical as well as mathematical approaches.
We also show that the dimensionality of the latent model, that is, the number of hidden variables in a system, can be calculated from the observed distribution.
We call the new distribution “Tanazur” and show through experiments that it is at least observed in one real world scenario, that of the motion of particles in an ideal gas.
We show that the Maxwell-Boltzmann distribution of particle speeds can be explained on the basis of Tanazur distributions.
American Psychological Association (APA)
Razzaq, Shahid& Khalid, Shehzad. 2015. Determination of System Dimensionality from Observing Near-Normal Distributions. Abstract and Applied Analysis،Vol. 2015, no. 2015, pp.1-17.
https://search.emarefa.net/detail/BIM-1052051
Modern Language Association (MLA)
Razzaq, Shahid& Khalid, Shehzad. Determination of System Dimensionality from Observing Near-Normal Distributions. Abstract and Applied Analysis No. 2015 (2015), pp.1-17.
https://search.emarefa.net/detail/BIM-1052051
American Medical Association (AMA)
Razzaq, Shahid& Khalid, Shehzad. Determination of System Dimensionality from Observing Near-Normal Distributions. Abstract and Applied Analysis. 2015. Vol. 2015, no. 2015, pp.1-17.
https://search.emarefa.net/detail/BIM-1052051
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1052051