| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1867036 | Physics Letters A | 2012 | 4 Pages |
Generalized Leibniz triangles have been used in nonextensive statistical mechanics as theoretical models that yield q -Gaussians (q<1q<1) as attractors. We study such triangles from a probability point of view. Our results show that one can get any distribution on [0,1][0,1] (or any distribution that has a compact support, after a linear transform) from such triangles, including q -Gaussians with q<1q<1. Next we propose conceptual models that are triangular arrays of row-wise exchangeable random variables and yield q -Gaussians for q<1q<1 and q⩾1q⩾1 as attractors, via laws of large numbers and central limit theorems, respectively.
► The theory of exchangeability is used to study the generalized Leibniz triangles. ► We explain how q -Gaussians (q<1q<1) are obtained by the triangles in a broader sense. ► We construct a model that can be applied to nonextensive statistical mechanics. ► The results provide a way of simulating any distribution on [0,1][0,1] with known moments.
