Quantiles for the Equicorrelated Multivariate-t Distribution

DESCRIPTION:

Computes a quantile of a pivotal quantity for use in multiple comparisons.

USAGE:

qmvt(p, k, df, rho, two.sided=T) 

REQUIRED ARGUMENTS:

p
the probability lying below the desired quantile.
k
a scalar, the dimension of the multivariate-t random vector; missing values and Infs are not allowed.
df
an integer, the error degrees of freedom. Inf is accepted (though specifying df=Inf will result in the use of df=1000). Missing values are not allowed.
rho
a (nonnegative) scalar, the common correlation coefficient of the underlying normally distributed variates.

OPTIONAL ARGUMENTS:

two.sided
a logical value, if TRUE a two-sided value is computed.

VALUE:

the pth quantile of the distribution of the pivotal quantity specified below.

DETAILS:

Suppose Z1, Z2, ... Zk are normal variables with means 0, variances 1, and common correlation rho>=0. Let U be a random variable independent of the X's, such that df*U^2 is Chisquare with df degrees of freedom. The two sided pivotal quantity is defined to be D = max{1<=i<=k: |Zi|/U }, The one-sided pivotal quantity is the above without absolute values.

The function obtains the critical point by numerical integration and a secant method. The Sidak multiple comparison method uses qmvt with rho=0.

REFERENCES:

Hochberg, Y. and Tamhane, A. C. (1987). Multiple Comparison Procedures. Wiley, New York.

Hsu, Jason C. (1996). Multiple Comparisons: Theory and Methods. Chapman and Hall, London.

SEE ALSO:

, , , .

EXAMPLES:

qmvt(.90, 20, 60, 0) 
qmvt(.99, 9, 20, .5, two.side=F)