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Stable distributions are a class of probability distributions allowing skewness and heavy tails (Rimmer and Nolan 2005). They are described by an index of stability (also ...

For two random variates X and Y, the correlation is defined bY cor(X,Y)=(cov(X,Y))/(sigma_Xsigma_Y), (1) where sigma_X denotes standard deviation and cov(X,Y) is the ...

Doob (1996) defines a stochastic process as a family of random variables {x(t,-),t in J} from some probability space (S,S,P) into a state space (S^',S^'). Here, J is the ...

The sequence of variates X_i with corresponding means mu_i obeys the strong law of large numbers if, to every pair epsilon,delta>0, there corresponds an N such that there is ...

The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 2000, p. 6). The survival function is therefore ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

The triangular distribution is a continuous distribution defined on the range x in [a,b] with probability density function P(x)={(2(x-a))/((b-a)(c-a)) for a<=x<=c; ...

The theory of point sets and sequences having a uniform distribution. Uniform distribution theory is important in modeling and simulation, and especially in so-called Monte ...

Let X_1, ..., X_N be a sequence of independent observations of a random variable X, and let the number of observations N itself be chosen at random. Then Wald's equation ...

A sequence of uncorrelated numbers alpha_n developed by Wiener (1926-1927). The numbers are constructed by beginning with {1,-1}, (1) then forming the outer product with ...