The Multivariate Normal and t Distributions, and Their Truncated Versions

Functions are provided for computing the density and the distribution function of d-dimensional normal and "t" random variables, possibly truncated (on one side or two sides), and for generating random vectors sampled from these distributions, except sampling from the truncated "t". Moments of arbitrary order of a multivariate truncated normal are computed, and converted to cumulants up to order 4. Probabilities are computed via non-Monte Carlo methods; different routines are used in the case d=1, d=2, d=3, d>3, if d denotes the dimensionality.


R package 'mnormt' history file

2005-nov. : built private version. 2006-01-23: 1.0-0 first version uploaded on CRAN. 2006-04-26: 1.0-1 fixed a bug of non-compliance to R programming standards. 2006-10-09: 1.1-0 adopt amedend Fortran code of Alan Genz (subtroutine TRESTR). 2006-10-26: 1.2-0 fixed a bug in function rmt. 2007-03-16: 1.2-1 some amendments in documentation. 2008-06-12: 1.3-0 added Fortran code for the bivariate case; improved R coding. 2009-01-26: 1.3-2 minor modification to F77 code to avoid GOTO out of IF block. 2009-03-21: 1.3-3 removed check on the R version on request of the R Core team. 2009-11-25: 1.3-4 fixed a bug affecting the case d>2 & df=Inf. 2011-01-16: 1.4-0 pd.solve() introduced; argument 'mean' can now be a matrix for {d,p}mnorm and {d,p}mt. 2011-04-06: 1.4-1 fixed documentation; coding of dmnorm & dmt is straightened; log.det in pd.solve() is returned only on request. 2011-04-28: 1.4-2 fixed bug of biv.not.prob if some (lower=-Inf & upper=Inf). 2011-05-03: 1.4-3 fixed bug as above for sadmvn and sadmvt. 2012-01-06: 1.4-5 NAMESPACE introduced on request by the R Core Team. 2013-12-04: 1.4-7 .First.lib() removed on request from CRAN, other minor fixes. 2014-06-25: 1.5-0 improved coding of dmnorm and dmt functions (avoids 'apply'); allow calling pmnorm and pmt with a matrix argument 'x'. 2014-06-30: 1.5-1 fixes a bug of parameter checking in dmnorm and dmt 2015-04-02: 1.5-2 new argument 'sqrt' of dmnorm and dmt; limited check of the arguments is introduced (earlier skipped for speed); calls to rmt with a smaller/larger of 'n' generate a sub/superset of values. 2015-05-25: 1.5-3 rmt and rmnorm output with d=1 have now the same structure; improved checks on arguments supplied to dmnorm and dmt.
2016-03-08: 1.5-4 improved NAMESPACE and documentation; more flexible use of mean in {d,p,r}mnorm and {d,p,r}mt; pd.solve transfers dimnames(x) to output. 2016-10-15: 1.5-5 fix a bug in rmt

Reference manual

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2.0.2 by Adelchi Azzalini, a year ago

Browse source code at

Authors: Adelchi Azzalini [aut, cre] , Alan Genz [aut] (most Fortran code) , Alan Miller [ctb] (Fortran routine PHI) , Michael J. Wichura [ctb] (Fortran routine PHINV) , G. W. Hill [ctb] (Fortran routine STDINV) , Yihong Ge [ctb] (Fortran routines BNVU and MVBVU).

Documentation:   PDF Manual  

Task views: Probability Distributions, Multivariate Statistics

GPL-2 | GPL-3 license

Imports tmvnsim

Imported by ARpLMEC, BayesCR, BifactorIndicesCalculator, ContaminatedMixt, DesignCTPB, DiceOptim, EMbC, ERP, EasyABC, FADA, GJRM, GLMaSPU, ICAOD, MBESS, MBSGS, MixedPsy, Rgbp, SIBER, SurvGSD, UPG, WACS, apollo, bapred, bgsmtr, blavaan, correctedAUC, derivmkts, dispRity, ei, highmean, latentcor, lavaan, ldbod, lmmpar, mixAK, mixedCCA, mvord, mvst, paleoTS, phytools, pmcgd, psych, sn, ssmn, tsDyn, wCorr.

Depended on by EXRQ, FAMT, MaXact, PAGWAS, PEACH, PLordprob, StratSel, Sunder, bayess, blatent, mdsdt, qtlhot, quantreg.nonpar, siar.

Suggested by BLCOP, brms, copent, fAssets, misty, rpact, semTools, vita.

See at CRAN