popKorn (version 0.3-0)

exactCoverageProb: Evaluate exact coverage probability

Description

This function will evaluate the exact coverage probability, as given in equation (4) on page 7 of the paper. See Details section.

Usage

exactCoverageProb(c.vec, theta.diff, lambda, c.val, sigma.2 = 1, n = 1)

Arguments

c.vec

This is a vector of length 2. It consists of the lower and upper limits in the integral. Checking is carried out to ensure that is of length two, and that 0 <= c.vec[1]="" <="c.vec[2]." this="" parameter="" is="" ignored="" if="" lambda is not missing.

theta.diff

A vector of length p-1, where p is the number of populations of treatments. Coordinate [i] in theta.diff corresponds to $\theta_i - \theta_{i+1}$. See genDelMat.

lambda

In case the user wishes to use the shrinkage version, this parameter should be specified. It must be between 0 and 1.

c.val

In case lambda is specified, this must not be missing. This will be combined with lambda to create a c.vec. This very function will then call itself.

sigma.2

The known variance of the error terms.

n

The number of replications per population.

Value

The function returns a scalar value that is the value of the exact coverage coverage probability defined in equation (4) of page 7.

Details

This function evaluates the coverage probability for an interval defined by $(X_{(1)} - c_2, X_{(1)} + c_1)$. Note that, as specified in the reference paper, we must have that $0 \le c_1 \le c_2$. This function will call integrate2. Please note the ordering of the elements in the c.vec argument: the first element corresponds to the upper limit of the interval, and to the negative of the lower limit of the integral.

See Also

integrate2, integrand

Examples

del1 <- c(2, 4)
exactCoverageProb(c(1.1,1.3), del1)
exactCoverageProb(theta.diff=c(2,3,4), lambda=0.9, c.val=2)