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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.

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 ...

This distribution is implemented in the Wolfram Language as InverseChiSquareDistribution[nu].

A fair coin is tossed an even 2n number of times. Let D=|H-T| be the absolute difference in the number of heads and tails obtained. Then the probability distribution is given ...

A transformation which transforms from a two-dimensional continuous uniform distribution to a two-dimensional bivariate normal distribution (or complex normal distribution). ...

The noncentral chi-squared distribution with noncentrality parameter lambda is given by P_r(x) = ...

A polynomial is called unimodal if the sequence of its coefficients is unimodal. If P(x) is log-convex and Q(x) is unimodal, then P(x)Q(x) is unimodal.

A correction to a discrete binomial distribution to approximate a continuous distribution. P(a<=X<=b) approx P((a-1/2-np)/(sqrt(np(1-p)))<=z<=(b+1/2-np)/(sqrt(np(1-p)))), ...

A foliation F of dimension p on a manifold M is transversely orientable if it is integral to a p-plane distribution D on M whose normal bundle Q is orientable. A p-plane ...