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Let A be a sum of squares of n independent normal standardized variates X_i, and suppose A=B+C where B is a quadratic form in the x_i, distributed as chi-squared with h ...

Let r be the correlation coefficient. Then defining z^'=tanh^(-1)r (1) zeta=tanh^(-1)rho, (2) gives sigma_(z^') = (N-3)^(-1/2) (3) var(z^') = 1/n+(4-rho^2)/(2n^2)+... (4) ...

The Gaussian joint variable theorem, also called the multivariate theorem, states that given an even number of variates from a normal distribution with means all 0, (1) etc. ...

The hazard function (also known as the failure rate, hazard rate, or force of mortality) h(x) is the ratio of the probability density function P(x) to the survival function ...

Let W(u) be a Wiener process. Then where V_t=f(W(t),tau) for 0<=tau=T-t<=T, and f in C^(2,1)((0,infty)×[0,T]). Note that while Ito's lemma was proved by Kiyoshi Ito (also ...

A joint distribution function is a distribution function D(x,y) in two variables defined by D(x,y) = P(X<=x,Y<=y) (1) D_x(x) = lim_(y->infty)D(x,y) (2) D_y(y) = ...

Let Q_i denote anything subject to weighting by a normalized linear scheme of weights that sum to unity in a set W. The Kolmogorov axioms state that 1. For every Q_i in W, ...

A statistic defined to improve the Kolmogorov-Smirnov test in the tails.

A discrete distribution of a random variable such that every possible value can be represented in the form a+bn, where a,b!=0 and n is an integer.

Given a function of the form y=a+blnx, (1) the coefficients can be found from least squares fitting as b = ...