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In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...

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 ...

Given a sequence of values {a_k}_(k=1)^n, the high-water marks are the values at which the running maximum increases. For example, given a sequence (3,5,7,8,8,5,7,9,2,5) with ...

A statistic which assigns a single number to several individual statistics in order to quantify trends. The best-known index in the United States is the consumer price index, ...

A system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), ...

Consider the Fibonacci-like recurrence a_n=+/-a_(n-1)+/-a_(n-2), (1) where a_0=0, a_1=1, and each sign is chosen independently and at random with probability 1/2. ...

A correction which must be applied to the measured moments m_k obtained from normally distributed data which have been binned in order to obtain correct estimators mu^^_i for ...

The randomization of a deck of cards by repeated interleaving. More generally, a shuffle is a rearrangement of the elements in an ordered list. Shuffling by exactly ...

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

Let {f_n} and {a_n} be sequences with f_n>=f_(n+1)>0 for n=1, 2, ..., then |sum_(n=1)^ma_nf_n|<=Af_1, where A=max{|a_1|,|a_1+a_2|,...,|a_1+a_2+...+a_m|}.