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The Zipf distribution, sometimes referred to as the zeta distribution, is a discrete distribution commonly used in linguistics, insurance, and the modelling of rare events. ...

The h-statistic h_r is the unique symmetric unbiased estimator for a central moment of a distribution <h_r>=mu_r. (1) In addition, the variance var(h_r)=<(h_r-mu_r)^2> (2) is ...

A continuous distribution defined on the range x in [0,2pi) with probability density function P(x)=(e^(bcos(x-a)))/(2piI_0(b)), (1) where I_0(x) is a modified Bessel function ...

The distinct prime factors of a positive integer n>=2 are defined as the omega(n) numbers p_1, ..., p_(omega(n)) in the prime factorization ...

A prime factor is a factor that is prime, i.e., one that cannot itself be factored. In general, a prime factorization takes the form ...

The Bernoulli distribution is a discrete distribution having two possible outcomes labelled by n=0 and n=1 in which n=1 ("success") occurs with probability p and n=0 ...

If F(x) is a probability distribution with zero mean and rho=int_(-infty)^infty|x|^3dF(x)<infty, (1) where the above integral is a stieltjes integral, then for all x and n, ...

A general type of statistical distribution which is related to the gamma distribution. Beta distributions have two free parameters, which are labeled according to one of two ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

The Gini coefficient (or Gini ratio) G is a summary statistic of the Lorenz curve and a measure of inequality in a population. The Gini coefficient is most easily calculated ...