On a Characterization of Uniform Distributions

On the Influence of Uniform Singularity Distributions

Exact expressions for three-dimensional potential and force field due to uniform singularity distributed on a finite flat rectangular surface have been presented. The expressions, valid throughout the physical domain, have been found to be consistent with other expressions available as special cases of the same problem. Very accurate estimates of the capacitance of a unit square plate and a uni...

Uniform Distributions on the Natural Numbers

We compare the following three notions of uniformity for a finitely additive probability measure on the set of natural numbers: that it extend limiting relative frequency, that it be shift-invariant, and that it map every residue class mod m to 1/m. We find that these three types of uniformity can be naturally ordered. In particular, we prove that the set L of extensions of limiting relative fr...

Quantization for uniform distributions on equilateral triangles

We approximate the uniform measure on an equilateral triangle by a measure supported on n points. We find the optimal sets of points (n-means) and corresponding approximation (quantization) error for n ≤ 4, give numerical optimization results for n ≤ 21, and a bound on the quantization error for n → ∞. The equilateral triangle has particularly efficient quantizations due to its connection with ...

A Class of Symmetric Bivariate Uniform Distributions

A class of symmetric bivariate uniform distributions is proposed for use in statistical modeling. The distributions may be constructed to be absolutely continuous with correlations as close to ±1 as desired. Expressions for the correlations, regressions and copulas are found. An extension to three dimensions is proposed.

Some New Characterization Results on Exponential and Related Distributions