| dmt {mnormt} | R Documentation |
The probability density function, the distribution function and random number generation for the multivariate t probability distribution
dmt(x, mean = rep(0, d), S, df=Inf, log = FALSE) pmt(x, mean = rep(0, length(x)), S, df=Inf, ...) rmt(n = 1, mean = rep(0, d), S, df=Inf) sadmvt(df, lower, upper, mean, S, maxpts = 2000 * d, abseps = 1e-06, releps = 0) biv.nt.prob(df, lower, upper, mean, S)
x |
for |
mean |
a numeric vector representing the location parameter
of the distribution (equal to the expected value when |
S |
a positive definite matrix representing the
scale matrix of the distribution, such that |
df |
degrees of freedom; it must be a positive integer for
|
log |
a logical value; if |
... |
parameters passed to |
n |
the number of random numbers to be generated |
lower |
a numeric vector of lower integration limits of
the density function; must be of maximal length 20;
|
upper |
a numeric vector of upper integration limits
of the density function; must be of maximal length 20;
|
maxpts |
the maximum number of function evaluations
(default value: |
abseps |
absolute error tolerance (default value: |
releps |
relative error tolerance (default value: |
The functions sadmvt and biv.nt.prob are interfaces to
Fortran-77 routines by Alan Genz, and available from his web page;
they makes uses of some auxiliary functions whose authors are
documented in the Fortran code. The routine sadmvt uses an adaptive
integration method. The routine biv.nt.prob is specific for the
bivariate case; if df<1 or df=Inf, it computes the bivariate
normal distribution function using a non-iterative method described in a
reference given below.
If pmt is called with d>2, this is converted into
a suitable call to sadmvt; if d=2, a call to
biv.nt.prob is used; if d=1, then pt is used.
dmt returns a vector of density values (possibly log-transformed);
pmt and sadmvt return a single probability with
attributes giving details on the achieved accuracy;
rmt returns a matrix of n rows of random vectors
The attributes error and status of the probability
returned by pmt and sadmvt indicate whether the function
had a normal termination, achieving the required accuracy. If
this is not the case, re-run the function with an higher value of
maxpts
Fortran code of SADMVT and most auxiliary functions by Alan Genz,
some additional auxiliary functions by people referred to within his
program. Porting to R and additional R code by Adelchi Azzalini
Genz, A.: Fortran code in files mvt.f and mvtdstpack.f
available at http://www.math.wsu.edu/math/faculty/genz/software/
Dunnett, C.W. and Sobel, M. (1954). A bivariate generalization of Student's t-distribution with tables for certain special cases. Biometrika 41, 153–169.
x <- seq(-2,4,length=21) y <- 2*x+10 z <- x+cos(y) mu <- c(1,12,2) Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3) df <- 4 f <- dmt(cbind(x,y,z), mu, Sigma,df) p1 <- pmt(c(2,11,3), mu, Sigma, df) p2 <- pmt(c(2,11,3), mu, Sigma, df, maxpts=10000, abseps=1e-8) x <- rmt(10, mu, Sigma, df) p <- sadmvt(df, lower=c(2,11,3), upper=rep(Inf,3), mu, Sigma) # upper tail # p0 <- pmt(c(2,11), mu[1:2], Sigma[1:2,1:2], df=5) p1 <- biv.nt.prob(5, lower=rep(-Inf,2), upper=c(2, 11), mu[1:2], Sigma[1:2,1:2]) p2 <- sadmvt(5, lower=rep(-Inf,2), upper=c(2, 11), mu[1:2], Sigma[1:2,1:2]) c(p0, p1, p2, p0-p1, p0-p2)