toms725, a Fortran77 code which evaluates multivariate normal integrals associated with the computation of cumulative probability density function (CDF) associated with a multidimensional variable governed by a normal probability density function (PDF) with a known correlation matrix, by Zvi Drezner. This is a version of ACM TOMS algorithm 725.
In particular, we wish to compute the probability P(H,R) that a sample vector X will satisfy
x(i) <= h(i) for 1 <= i <= m
which is
1/sqrt(2^m*pi^m*det(R)) *
integral (-oo < x(m) < h(m) ) *
...
integral (-oo < x(2) < h(2) ) *
integral (-oo < x(1) < h(1) )
exp ( -0.5 * x' * inverse(R) * x ) dx1 dx2 ... dxm
The computer code and data files described and made available on this web page are distributed under the MIT license
toms725 is available in a FORTRAN77 version.
hermite_polynomial, a FORTRAN77 library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
prob, a FORTRAN77 library which evaluates, samples, inverts, and characterizes a number of Probability Density Functions (PDF's) and Cumulative Density Functions (CDF's), including anglit, arcsin, benford, birthday, bernoulli, beta_binomial, beta, binomial, bradford, burr, cardiod, cauchy, chi, chi squared, circular, cosine, deranged, dipole, dirichlet mixture, discrete, empirical, english sentence and word length, error, exponential, extreme values, f, fisk, folded normal, frechet, gamma, generalized logistic, geometric, gompertz, gumbel, half normal, hypergeometric, inverse gaussian, laplace, levy, logistic, log normal, log series, log uniform, lorentz, maxwell, multinomial, nakagami, negative binomial, normal, pareto, planck, poisson, power, quasigeometric, rayleigh, reciprocal, runs, sech, semicircular, student t, triangle, uniform, von mises, weibull, zipf.