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A joint distribution function is a distribution function D(x,y) in two variables defined by D(x,y) = P(X<=x,Y<=y) (1) D_x(x) = lim_(y->infty)D(x,y) (2) D_y(y) = ...

A generalization of Student's t-distribution known as the noncentral Student's t-distribution is given by (1) where Gamma(z) is the gamma function and _1F_1(a;b;z) is a ...

There are essentially three types of Fisher-Tippett extreme value distributions. The most common is the type I distribution, which are sometimes referred to as Gumbel types ...

A variable with a beta binomial distribution is distributed as a binomial distribution with parameter p, where p is distribution with a beta distribution with parameters ...

A univariate distribution proportional to the F-distribution. If the vector d is Gaussian multivariate-distributed with zero mean and unit covariance matrix N_p(0,I) and M is ...

The negative binomial distribution, also known as the Pascal distribution or Pólya distribution, gives the probability of r-1 successes and x failures in x+r-1 trials, and ...

Let S_n be the set of permutations of {1, 2, ..., n}, and let sigma_t be the continuous time random walk on S_n that results when randomly chosen transpositions are performed ...

The theory of point sets and sequences having a uniform distribution. Uniform distribution theory is important in modeling and simulation, and especially in so-called Monte ...

A function giving the distribution of the interpoint distances of a curve. It is defined by p(r)=1/Nsum_(ij)delta_(r_(ij)=r).

For signed distances on a line segment, AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0, since (b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.