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A spatial-temporal point process is a point process which models data that is localized at a discrete set of locations in both space and time. In particular, a ...

The term "range" has two completely different meanings in statistics. Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j, the range of the random sample ...

The voter model is a simple mathematical model of opinion formation in which voters are located at the nodes of a network, each voter has an opinion (in the simplest case, 0 ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p) and numbers are assigned to the edges of a grid. A b-cluster is an ...

The Gauss-Kuzmin distribution is the distribution of occurrences of a positive integer k in the continued fraction of a random (or "generic") real number. Consider xi_n ...

In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...

Let a distribution to be approximated be the distribution F_n of standardized sums Y_n=(sum_(i=1)^(n)(X_i-X^_))/(sqrt(sum_(i=1)^(n)sigma_X^2)). (1) In the Charlier series, ...

Given two randomly chosen n×n integer matrices, what is the probability D(n) that the corresponding determinants are relatively prime? Hafner et al. (1993) showed that ...

A sufficient condition on the Lindeberg-Feller central limit theorem. Given random variates X_1, X_2, ..., let <X_i>=0, the variance sigma_i^2 of X_i be finite, and variance ...

Any method which solves a problem by generating suitable random numbers and observing that fraction of the numbers obeying some property or properties. The method is useful ...