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The Mann-Whitney test statistic is equivalent to the Wilcoxon test statistic (van der Waerden 1969).

A random process whose future probabilities are determined by its most recent values. A stochastic process x(t) is called Markov if for every n and t_1<t_2...<t_n, we have ...

A sequence X_1, X_2, ... of random variates is called Markov (or Markoff) if, for any n, F(X_n|X_(n-1),X_(n-2),...,X_1)=F(X_n|X_(n-1)), i.e., if the conditional distribution ...

If x takes only nonnegative values, then P(x>=a)<=(<x>)/a. (1) To prove the theorem, write <x> = int_0^inftyxP(x)dx (2) = int_0^axP(x)dx+int_a^inftyxP(x)dx. (3) Since P(x) is ...

A matrix each of whose elements is a variate. These variates need not be independent, and if they are not, a correlation is said to exist between them.

The approximating polynomial which has the smallest maximum deviation from the true function. It is closely approximated by the Chebyshev polynomials of the first kind.

A regression giving conditional expectation values of a given variable in terms of two or more other variables.

The term negative likelihood ratio is also used (especially in medicine) to test nonnested complementary hypotheses as follows, NLR = ([false negative rate])/([true negative ...

Let S be the set of all possibilities that satisfy hypothesis H, and let S^' be the set of all possibilities that satisfy hypothesis H^'. Then H^' is a nested hypothesis ...

If there exists a critical region C of size alpha and a nonnegative constant k such that (product_(i=1)^(n)f(x_i|theta_1))/(product_(i=1)^(n)f(x_i|theta_0))>=k for points in ...