scholarly journals A Characterization of Symmetric Stable Distributions

2016 ◽  
Vol 2016 ◽  
pp. 1-3
Author(s):  
Wiktor Ejsmont
Keyword(s):  
Characteristic Function ◽  
Normal Distribution ◽  
Linear Form ◽  
Stable Distributions

Characterization problems in probability are studied here. Using the characteristic function of an additive convolution we generalize some known characterizations of the normal distribution to stable distributions. More precisely, if a distribution of a linear form depends only on the sum of powers of the certain parameters, then we obtain symmetric stable distributions.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

A Characterization of Deviation from Normality Under Certain Moment Assumptions

1966 ◽  
Vol 9 (4) ◽  
pp. 509-514
Author(s):  
W.R. McGillivray ◽  
C.L. Kaller
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Standard Normal Distribution ◽  
Standard Normal ◽  
Image Position

If Fn is the distribution function of a distribution n with moments up to order n equal to those of the standard normal distribution, then from Kendall and Stuart [1, p.87],

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