The geometrical origins of some distributions and the complete
concentration of measure phenomenon for mean-values of functionals
C. Liu. (2017)cite arxiv:1705.01327Comment: 8 pages.
Abstract
We derive out naturally some important distributions such as high order
normal distributions and high order exponent distributions and the Gamma
distribution from a geometrical way. Further, we obtain the exact mean-values
of integral form functionals in the balls of continuous functions space with
$p-$norm, and show the complete concentration of measure phenomenon which means
that a functional takes its average on a ball with probability 1, from which we
have nonlinear exchange formula of expectation.
Description
The geometrical origins of some distributions and the complete
concentration of measure phenomenon for mean-values of functionals
%0 Generic
%1 liu2017geometrical
%A Liu, Cheng-shi
%D 2017
%K func-an maths thermod
%T The geometrical origins of some distributions and the complete
concentration of measure phenomenon for mean-values of functionals
%U http://arxiv.org/abs/1705.01327
%X We derive out naturally some important distributions such as high order
normal distributions and high order exponent distributions and the Gamma
distribution from a geometrical way. Further, we obtain the exact mean-values
of integral form functionals in the balls of continuous functions space with
$p-$norm, and show the complete concentration of measure phenomenon which means
that a functional takes its average on a ball with probability 1, from which we
have nonlinear exchange formula of expectation.
@misc{liu2017geometrical,
abstract = {We derive out naturally some important distributions such as high order
normal distributions and high order exponent distributions and the Gamma
distribution from a geometrical way. Further, we obtain the exact mean-values
of integral form functionals in the balls of continuous functions space with
$p-$norm, and show the complete concentration of measure phenomenon which means
that a functional takes its average on a ball with probability 1, from which we
have nonlinear exchange formula of expectation.},
added-at = {2017-05-04T23:46:41.000+0200},
author = {Liu, Cheng-shi},
biburl = {https://www.bibsonomy.org/bibtex/21f68f7e293af9d53f1f4de7527b7eaee/vindex10},
description = {The geometrical origins of some distributions and the complete
concentration of measure phenomenon for mean-values of functionals},
interhash = {a6b64566eed3a2c426fed1d3942dc67f},
intrahash = {1f68f7e293af9d53f1f4de7527b7eaee},
keywords = {func-an maths thermod},
note = {cite arxiv:1705.01327Comment: 8 pages},
timestamp = {2017-05-04T23:46:41.000+0200},
title = {The geometrical origins of some distributions and the complete
concentration of measure phenomenon for mean-values of functionals},
url = {http://arxiv.org/abs/1705.01327},
year = 2017
}