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A Vandermonde matrix is a type of matrix that arises in the polynomial least squares fitting, Lagrange interpolating polynomials (Hoffman and Kunze p. 114), and the ...

The Maxwell (or Maxwell-Boltzmann) distribution gives the distribution of speeds of molecules in thermal equilibrium as given by statistical mechanics. Defining a=sqrt(kT/m), ...

A theorem which specifies the structure of the generic unitary representation of the Weyl relations and thus establishes the equivalence of Heisenberg's matrix mechanics and ...

The distribution with probability density function and distribution function P(x) = (ab^a)/(x^(a+1)) (1) D(x) = 1-(b/x)^a (2) defined over the interval x>=b. It is ...

A statistical distribution for which the variables may take on a continuous range of values. Abramowitz and Stegun (1972, p. 930) give a table of the parameters of most ...

The logarithmic distribution is a continuous distribution for a variate X in [a,b] with probability function P(x)=(lnx)/(b(lnb-1)-a(lna-1)) (1) and distribution function ...

Given two distributions Y and X with joint probability density function f(x,y), let U=Y/X be the ratio distribution. Then the distribution function of u is D(u) = P(U<=u) (1) ...

Fischer's z-distribution is the general distribution defined by g(z)=(2n_1^(n_1/2)n_2^(n_2/2))/(B((n_1)/2,(n_2)/2))(e^(n_1z))/((n_1e^(2z)+n_2)^((n_1+n_2)/2)) (1) (Kenney and ...

A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times ...

F_k[P_N(k)](x)=F_k[exp(-N|k|^beta)](x), where F is the Fourier transform of the probability P_N(k) for N-step addition of random variables. Lévy showed that beta in (0,2) for ...