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Multivariate Normal CDF
Implements the multivariate normal CDF
Algorithm
Uses the algorithm as explained in Section 4.2.2 in Computation of Multivariate Normal and t Probabilities by Alan Genz and Frank Bretz, together with the cholesky decomposition with dynamic changing of rows explained in Section 4.1.3. Specifically we use a Quasi Monte Carlo method.
Additions
ContinuousMultivariateCDF
inmod.rs
MultivariateUniform
inmultivariate_uniform.rs
(mainly for me wanting an in-house way to get uniform distribution inmean
,mode
,pdf
,cdf
,min
,max
,ln_pdf
.chol_chrows
for computing the Cholesky decomposition dynamically whilst changing rows for better integration limitsintegrate_pdf
to integrate a multivariate pdf between limitsa
andb
ContinuousMultivariateCDF
forMultivariateNormal
(andMultivariateUniform
), wherecdf
usesintegrate_pdf
with left limita=[f64::NEG_INFINITY; dim]
and right limitx=b
cdf
againstscipy.stats.multivariate_normal.cdf
in python, as well asMvNormalCDF
in Juliaprimes
for generating first