Wigner quasi-probability densities and characterization of the Gaussian distribution

1999 ◽  
Vol 93 (3) ◽  
pp. 341-348
Author(s):  
A. A. Zinger
Keyword(s):  
Gaussian Distribution ◽  
Probability Densities

Some inequalities for moments and coefficients of variation for a large class of probability functions

1979 ◽  
Vol 16 (3) ◽  
pp. 665-670 ◽  
Author(s):  
Burt V. Bronk
Keyword(s):  
Large Class ◽  
Average Molecular Weight ◽  
Empirical Measure ◽  
Number Average Molecular Weight ◽  
Positive Real ◽  
Coefficients Of Variation ◽  
Probability Densities ◽  
Rigorous Bounds ◽  
Illustrative Application

Some inequalities for moments and coefficients of variation of probability densities over the positive real line are obtained by means of simple geometrical relationships. As an illustrative application rigorous bounds are obtained for the ratio of weight average to number average molecular weight for a large class of distributions of macromolecules, giving a more precise characterization of this empirical measure of heterogeneity.

Profile Characterization of Manufactured Surfaces Using Random Function Excursion Technique—Part 1: Theory

1975 ◽  
Vol 97 (1) ◽  
pp. 190-195 ◽  
Author(s):  
T. S. Sankar ◽  
M. O. M. Osman
Keyword(s):  
Surface Texture ◽  
Low Cost ◽  
Measuring Device ◽  
Rolling Circle ◽  
Measuring Devices ◽  
Texture Parameters ◽  
Probability Densities ◽  
On Line ◽  
Excursion Probability

This paper discusses a new approach for describing accurately the typology of manufactured surfaces. The method employs the theory of stochastic excursions to characterize the surface texture in the amplitude and lengthwise directions. The mathematical principle behind the approach is briefly explained, and it is shown that an accurate description of the roughness can be obtained from the knowledge of the intercept probabilities of the crest and valley excursions of the surface texture about any given level, say the CLA value, specified with respect to the mean line. Based on the preceding excursion probability densities, new surface texture parameters are proposed. These parameters may be computed directly from the surface roughness data obtained from commercially available measuring devices. On the basis of this investigation, it is feasible to develop a low-cost measuring device for “on-line” surface evaluation in production. It is also shown that the sampling length provides a geometrically well-defined filter characteristic similar to that of the rolling circle radius in the E-system.

Characterization of a class of second-order density functions

1967 ◽  
Vol 4 (1) ◽  
pp. 123-129 ◽  
Author(s):  
C. B. Mehr
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Gaussian Distribution ◽  
Random Variables ◽  
Second Order ◽  
Independent Random Variables ◽  
Density Functions ◽  
Linear Filtering ◽  
Non Linear

Distributions of some random variables have been characterized by independence of certain functions of these random variables. For example, let X and Y be two independent and identically distributed random variables having the gamma distribution. Laha showed that U = X + Y and V = X | Y are also independent random variables. Lukacs showed that U and V are independently distributed if, and only if, X and Y have the gamma distribution. Ferguson characterized the exponential distribution in terms of the independence of X – Y and min (X, Y). The best-known of these characterizations is that first proved by Kac which states that if random variables X and Y are independent, then X + Y and X – Y are independent if, and only if, X and Y are jointly Gaussian with the same variance. In this paper, Kac's hypotheses have been somewhat modified. In so doing, we obtain a larger class of distributions which we shall call class λ1. A subclass λ0 of λ1 enjoys many nice properties of the Gaussian distribution, in particular, in non-linear filtering.

scholarly journals Subdifferential characterization of probability functions under Gaussian distribution

2018 ◽  
Vol 174 (1-2) ◽  
pp. 167-194 ◽  
Author(s):  
Abderrahim Hantoute ◽  
René Henrion ◽  
Pedro Pérez-Aros
Keyword(s):  
Gaussian Distribution ◽  
Probability Functions

On a probability function useful in size modelling

1993 ◽  
Vol 23 (8) ◽  
pp. 1679-1683 ◽  
Author(s):  
M. Aslam Chaudhry ◽  
Munir Ahmad
Keyword(s):  
Differential Equation ◽  
Gaussian Distribution ◽  
Probability Function ◽  
Inverse Gaussian Distribution ◽  
Statistical Properties ◽  
Inverse Gaussian ◽  
Probability Densities ◽  
Present Distribution

A probability function has been derived as a solution to a generalized Pearson differential equation. Some statistical properties of the function are investigated. An interesting relationship between the present distribution and the inverse Gaussian distribution is stated. It is demonstrated that the function is more suitable than other probability densities in some applications of size models.

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