pcmvt {CondMVT}

Conditional Multivariate t Distribution

Description

Computes the distribution function of the conditional multivariate t, [Y given X], where Z = (X,Y) is the fully-joint multivariate t distribution with mean equal to location vector, df equal to degrees of freedom and scatter matrix sigma. Computations are based on algorithms by Genz and Bretz.

Usage

pcmvt(lower = -Inf, upper = Inf, mean, sigma, df, dependent.ind, given.ind, X.given,
check.sigma = TRUE, algorithm = GenzBretz(), ...)

Arguments

lower

the vector of lower limits of length n.

upper

the vector of upper limits of length n.

mean

the mean vector of length n.

sigma

a symmetric, positive-definte matrix, of dimension n x n, which must be specified.

df

degrees of freedom, which must be specified.

dependent.ind

a vector of integers denoting the indices of the dependent variable Y.

given.ind

a vector of integers denoting the indices of the conditioning variable X.

X.given

a vector of reals denoting the conditioning value of X. When both given.ind and X.given are missing, the distribution of Y becomes Z[dependent.ind]

check.sigma

logical; if TRUE, the variance-covariance matrix is checked for appropriateness (symmetry, positive-definiteness). This could be set to FALSE if the user knows it is appropriate.

algorithm

an object of class GenzBretz, Miwa or TVPACK specifying both the algorithm to be used as well as the associated hyper parameters.

...

additional parameters (currently given to GenzBretz for backward compatibility issues).

Details

This program involves the computation of multivariate t probabilities with arbitrary correlation matrices.

Value

The evaluated distribution function is returned with attributes

error

estimated absolute error and

msg

Normal Completion

References

Genz, A. and Bretz, F. (1999), Numerical computation of multivariate t-probabilities with application to power calculation of multiple contrasts. Journal of Statistical Computation and Simulation, 63, 361–378.

Genz, A. and Bretz, F. (2002), Methods for the computation of multivariate t-probabilities. Journal of Computational and Graphical Statistics, 11, 950–971.

Genz, A. (2004), Numerical computation of rectangular bivariate and trivariate normal and t-probabilities, Statistics and Computing, 14, 251–260.

Genz, A. and Bretz, F. (2009), Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195. Springer-Verlag, Heidelberg.

See Also

dcmvt(),rcmvt(),pmvt(),GenzBretz()

Examples

n <- 10
df=3
A <- matrix(rt(n^2,df), n, n)
A <- tcrossprod(A,A) #A %*% t(A)

pcmvt(lower=-Inf, upper=1, mean=rep(1,n), sigma=A, df=df,	dependent.ind=3, 
      given.ind=c(1,4,7,9,10), X.given=c(1,1,0,0,-1))


pcmvt(lower=-Inf, upper=c(1,2), mean=rep(1,n),
      sigma=A,df=df, dep=c(2,5), given=c(1,4,7,9,10),
      X=c(1,1,0,0,-1))

pcmvt(lower=-Inf, upper=c(1,2), mean=rep(1,n), sigma=A,df=df,
      dep=c(2,5))