Title: Mathematical, physical and physiological background of normal distribution, delta distribution and log-normal distribution

Authors: Chang Lin Zhang

Addresses: College of Life Science, Zhejiang University, Hangzhou, China; Department of Music and Music Education, Siegen University, Hochstrasse 57, Siegen D-57076, Germany

Abstract: The backgrounds of three statistical distributions of measurement data, namely, normal distribution, log-normal distribution and delta distribution are discussed here from the viewpoint of mathematics, physics and physiology. It can proved by means of combination mathematics that the measurement data which fit into normal distribution come from a system in ideal chaotic state; whereas, only the data from ideal crystal state fit into delta distribution. The most important distribution for physiological system, however, is log-normal distribution which shows that the measurement data come from a system that is in coherent state, in which every element keeps its independence and at the same time has the ability to cooperate with all others.

Keywords: normal distribution; log-normal distribution; delta distribution; chaotic state; coherent state; crystal state; mathematics; physics; physiology.

DOI: 10.1504/IJMIC.2008.023121

International Journal of Modelling, Identification and Control, 2008 Vol.5 No.3, pp.200 - 204

Available online: 10 Feb 2009 *

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