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Let there be N_i observations of the ith phenomenon, where i=1, ..., p and N = sumN_i (1) y^__i = 1/(N_i)sum_(alpha)y_(ialpha) (2) y^_ = 1/Nsum_(i)sum_(alpha)y_(ialpha). (3) ...

The difference of a quantity from some fixed value, usually the "correct" or "expected" one.

Discrepancy is a measure of the deviation of a point set from a uniform distribution. In general, the computation of the discrepancy of a point set is computationally ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

For any two ergodic measure-preserving transformations on nonatomic probability spaces, there is an isomorphism between the two probability spaces carrying orbits onto orbits.

A roll of eight on a pair of six-sided dice in the game of craps. The probability of rolling "eighter from Decatur" is 5/36, or 13.888...%.

A distribution of error such that the error remaining is always given approximately by the last term dropped.

A normal distribution with mean 0, P(x)=h/(sqrt(pi))e^(-h^2x^2). (1) The characteristic function is phi(t)=e^(-t^2/(4h^2)). (2) The mean, variance, skewness, and kurtosis ...

An estimator is a rule that tells how to calculate an estimate based on the measurements contained in a sample. For example, the sample mean x^_ is an estimator for the ...

The bias of an estimator theta^~ is defined as B(theta^~)=<theta^~>-theta. (1) It is therefore true that theta^~-theta = (theta^~-<theta^~>)+(<theta^~>-theta) (2) = ...