toms725


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
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

toms725 is available in a FORTRAN77 version.

Related Data and Programs:

toms725_test

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.

Reference:

  1. Zvi Drezner,
    Algorithm 725: Computation of the Multivariate Normal Integral,
    Transactions on Mathematical Software,
    Volume 18, Number 4, December 1992, pages 470-480.

Source Code:


Last revised on 01 December 2023.