A characterization of the normal distribution based on the sample mean and the residual vector

1978 ◽  
Vol 29 (2) ◽  
pp. 77-80
Author(s):  
R. Ahmad
Keyword(s):  
Normal Distribution ◽  
Residual Vector ◽  
Sample Mean

A NEW CHARACTERIZATION OF THE NORMAL DISTRIBUTION AND TEST FOR NORMALITY

2015 ◽  
Vol 32 (5) ◽  
pp. 1216-1252 ◽  
Author(s):  
Anil K. Bera ◽  
Antonio F. Galvao ◽  
Liang Wang ◽  
Zhijie Xiao
Keyword(s):  
Normal Distribution ◽  
Testing Procedure ◽  
Finite Sample ◽  
Omnibus Test ◽  
Sample Mean ◽  
Underlying Distribution ◽  
Asymptotic Covariance ◽  
Finite Sample Properties ◽  
Test For Normality

We study the asymptotic covariance function of the sample mean and quantile, and derive a new and surprising characterization of the normal distribution: the asymptotic covariance between the sample mean and quantile is constant across all quantiles,if and only ifthe underlying distribution is normal. This is a powerful result and facilitates statistical inference. Utilizing this result, we develop a new omnibus test for normality based on the quantile-mean covariance process. Compared to existing normality tests, the proposed testing procedure has several important attractive features. Monte Carlo evidence shows that the proposed test possesses good finite sample properties. In addition to the formal test, we suggest a graphical procedure that is easy to implement and visualize in practice. Finally, we illustrate the use of the suggested techniques with an application to stock return datasets.

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.

A note on the characterization of the multivariate normal distribution

Metrika ◽  
1979 ◽  
Vol 26 (1) ◽  
pp. 25-30 ◽  
Author(s):  
Sh. Talwalker
Keyword(s):  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal

A methodology for normal distribution-based statistical characterization of long-term insolation by means of historical data

Solar Energy ◽  
2015 ◽  
Vol 122 ◽  
pp. 440-454 ◽  
Author(s):  
Almir Sedić ◽  
Danijel Pavković ◽  
Mihajlo Firak
Keyword(s):  
Normal Distribution ◽  
Historical Data ◽  
Statistical Characterization

Characterization of Half-Normal Distribution Based on Linear Combinations of Order Statistics

2001 ◽  
Vol 51 (1-2) ◽  
pp. 113-118
Author(s):  
P. Yageen Thomas ◽  
N.V. Sreekumar
Keyword(s):  
Normal Distribution ◽  
Order Statistics ◽  
Linear Combinations

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],

scholarly journals The Alpha stable distribution in ocean ambient noise modelling

2019 ◽  
Vol 283 ◽  
pp. 08002
Author(s):  
Guoli Song ◽  
Xinyi Guo ◽  
Li Ma
Keyword(s):  
Normal Distribution ◽  
Ambient Noise ◽  
Stable Distribution ◽  
Characteristic Exponent ◽  
Statistical Modelling ◽  
Gaussian State ◽  
Sample Mean ◽  
Noise Interference ◽  
Interference Noise ◽  
Non Gaussian

In view of the non-Gaussian of ocean ambient noise, the  stable distribution is applied to the statistical modelling. Firstly, the one-to-one correspondence between the four parameters of stable distribution and the sample mean, variance, skewness and kurtosis are established according to physical meaning. Then, numerical simulations are conducted to analyze the suitability of stable distribution for non-Gaussian ambient noise. In the case of white noise interference, noise is divided into Gaussian state, leptokurtic, and platykurtic separately. The parameters of stable distribution are estimated by the sample quantile and characteristic function method jointly. The simulation results show that, in the Gaussian state,  stable distribution is equivalent to normal distribution. As for leptokurtic distribution, stable distribution is much better than normal distribution, indicating absolute predominance in impulse-like data modeling. But it is not adaptive for low kurtosis state because its characteristic exponent can’t be bigger than two. Finally, the result is verified by ambient noise collected in three environmental conditions, such as quiet ambient noise, airgun interference noise and ship noise. In all three cases,  stable distribution shows good adaptability and accuracy, especially for the airgun dataset it is far superior to normal distribution.

Sign in / Sign up

Export Citation Format

Share Document