A characterization of the generalized Laplace distribution by constant regression on the sample mean

2016 ◽  
Vol 113 ◽  
pp. 79-83
Author(s):  
Shaul K. Bar-Lev ◽  
Daoud Bshouty
Keyword(s):  
Laplace Distribution ◽  
Sample Mean ◽  
Constant Regression

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 Monophyletic clustering and characterization of protein families

2007 ◽  
Vol 4 (3) ◽  
pp. 89-100 ◽  
Author(s):  
Jian Zhang ◽  
Zhiyuan Zhao ◽  
Jennifer Evershed ◽  
Guoying Li
Keyword(s):  
Software Package ◽  
Sequence Similarity ◽  
Correlation Coefficients ◽  
Protein Family ◽  
Clustering Methods ◽  
Clustering Method ◽  
Protein Families ◽  
Sample Mean ◽  
Mean And Variance

Summary A protein family contains sequences that are evolutionarily related. Generally, this is reflected by sequence similarity. There have been many attempts to organize the set of protein families into evolutionarily homogenous clusters using certain clustering methods. How do we characterize these clusters? How can we cluster protein families using these characterizations? In this work, these questions were addressed by use of a concept called group-wide co-evolution, and was exemplified by some real and simulated protein family data. The results have shown that the trend of a group of monophyletic proteins might be characterized by a normal distribution, while the strength and variability of this trend can be described by the sample mean and variance of the observed correlation coefficients after a suitable transformation. To exploit this property, we have developed a monophyletic clustering method called monophyletic k−medoids clustering. A software package written in R has been made available at http://www.kent.ac.uk/ims/personal/jz .

When Does a Quadratic Statistic Have a Constant Regression on a Sample Mean?

1980 ◽  
Vol 24 (3) ◽  
pp. 649-651
Author(s):  
L. B. Klebanov
Keyword(s):  
Sample Mean ◽  
Constant Regression

Constant regression of quadratic statistics on the sample mean

1977 ◽  
Vol 3 (1) ◽  
pp. 51-53 ◽  
Author(s):  
B. Gyires
Keyword(s):  
Sample Mean ◽  
Constant Regression

scholarly journals A constant regression characterization of the gamma law

1990 ◽  
Vol 22 (02) ◽  
pp. 488-490
Author(s):  
Jacek Wesołowski
Keyword(s):  
Gamma Distribution ◽  
Characteristic Property ◽  
Random Variables ◽  
Constant Regression ◽  
Gamma Law

A constant regression of the quotient on the sum of two i.i.d. non-degenerate positive random variables is a characteristic property of the gamma distribution.

A characterization of the uniform distribution on the circle in the analysis of directional data

1978 ◽  
Vol 15 (4) ◽  
pp. 852-857
Author(s):  
M. S. Bingham
Keyword(s):  
Uniform Distribution ◽  
Directional Data ◽  
Regularity Conditions ◽  
Sample Sizes ◽  
Fixed Size ◽  
Sample Mean ◽  
Random Samples ◽  
Resultant Length

It was conjectured some time ago by K. V. Mardia that if, for random samples of some fixed size N ≧ 2 from a given non-degenerate circular population, the sample mean direction and the sample resultant length are independently distributed, then the population must be uniformly distributed round the circle. In this paper it is shown that, apart from one minor exception, Mardia's conjecture is true in the case N = 2. No regularity conditions are necessary for the proof. The same problem has been studied, subject to regularity conditions, by Kent, Mardia and Rao (1976) for all sample sizes N ≧ 2 except N = 4.

A characterization of the uniform distribution on the circle in the analysis of directional data

1978 ◽  
Vol 15 (04) ◽  
pp. 852-857
Author(s):  
M. S. Bingham
Keyword(s):  
Uniform Distribution ◽  
Directional Data ◽  
Regularity Conditions ◽  
Sample Sizes ◽  
Fixed Size ◽  
Sample Mean ◽  
Random Samples ◽  
Resultant Length

It was conjectured some time ago by K. V. Mardia that if, for random samples of some fixed size N ≧ 2 from a given non-degenerate circular population, the sample mean direction and the sample resultant length are independently distributed, then the population must be uniformly distributed round the circle. In this paper it is shown that, apart from one minor exception, Mardia's conjecture is true in the case N = 2. No regularity conditions are necessary for the proof. The same problem has been studied, subject to regularity conditions, by Kent, Mardia and Rao (1976) for all sample sizes N ≧ 2 except N = 4.

scholarly journals On a Characterization of the Wiener Process by Constant Regression

1970 ◽  
Vol 41 (1) ◽  
pp. 321-325 ◽  
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Wiener Process ◽  
Constant Regression

scholarly journals A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Werner Hürlimann
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Gamma Distribution ◽  
Random Sums ◽  
Likelihood Estimator ◽  
Sample Mean ◽  
Count Distribution ◽  
Compound Distribution ◽  
The Mean

We consider the class of those distributions that satisfy Gauss's principle (the maximum likelihood estimator of the mean is the sample mean) and have a parameter orthogonal to the mean. It is shown that this so-called “mean orthogonal class” is closed under convolution. A previous characterization of the compound gamma characterization of random sums is revisited and clarified. A new characterization of the compound distribution with multiparameter Hermite count distribution and gamma severity distribution is obtained.

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