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)
x |
for dmt , this is either a vector of length d
or a matrix with d columns, where d=ncol(S) , giving
the coordinates of the point(s) where the density must be evaluated;
for pmt , only a vector of length d is allowed,
and d cannot exceed 20 |
mean |
a numeric vector representing the location parameter
of the distribution (equal to the expected value when df>1 );
it must be of length d , as defined above |
S |
a positive definite matrix representing the
scale matrix of the distribution, such that S*df/(df-2) is
the variance-covariance matrix when df>2 ;
a vector of length 1 is also allowed
(in this case, d=1 is set) |
df |
degrees of freedom; it must be a positive integer for
pmt and sadmvt , otherwise a positive number; if
df=Inf (default value), the corresponding *mnorm
function is called |
log |
a logical value; if TRUE ,
the logarithm of the density is computed
|
... |
parameters passed to sadmvt ,
among maxpts , absrel , releps |
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;
+Inf and -Inf entries are allowed |
upper |
a numeric vector of upper integration limits
of the density function; must be of maximal length 20;
+Inf and -Inf entries are allowed |
maxpts |
the maximum number of function evaluations
(default value: 2000*d ) |
abseps |
absolute error tolerance (default value: 1e-6 ) |
releps |
relative error tolerance (default value: 0 ) |
Function sadmvt
is an interface to a Fortran-77 routine with
the same name written by Alan Genz, and available from his web page;
this makes uses of some auxiliary functions whose authors are
documented in the Fortran code. The routine uses an adaptive
integration method.
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 available at http://www.math.wsu.edu/math/faculty/genz/software/mvt.f
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