popKorn (version 0.3-0)

eqnForMin: Evaluate the function to be minimised

Description

This will evaluate the appropriate function for determining the c value in the confidence interval for $X_(1)$.

Usage

eqnForMin(c.val, lambda = 0.5, alpha = 0.05, min.loc = "infty", n, p, k = 1, var.known = TRUE)

Arguments

c.val

The value at which to evaluate the appropriate function.

lambda

The value of lambda under consideration. This must be a scalar between 0 and 1.

alpha

The desired confidence coefficient.

min.loc

The location of the minimum, either at 'zero' or 'infty'.

n

The number of replications per population.

p

The number of populations considered. This must be present if min.loc is equal to 'zero'.

k

The number of populations selected.

var.known

A logical flag indicating if the variance of the observations is known exactly. It is TRUE by default.

Value

The function returns a scalar value.

Details

This function will choose the correct equation to use for determining the smallest c-value that maintains the desired coverage probability. Note that this function does *not* do the minimization. That procedure is done by optimalC.

There are essentially 8 different cases to consider. They correspond to the cases when the variance is known or unknown, when the number of populations selected is greater than 1 or equal to 1, and when the minimum of the equation is located at infinity or 0.