umpu.binom: UMPU Test for the Binomial Distribution
Description
Calculate the uniformly most powerful unbiased (UMPU) two-tailed test
for the binomial distribution.
Usage
umpu.binom(x, n, p, alpha, maxiter = 10, tol = 1e-9)
Arguments
x
binomial observations.
n
number of observations.
p
the success probability under the null hypothesis.
alpha
the significance level.
maxiter
the maximum number of iterations allowed.
tol
tolerance used in testing floating point numbers.
Value
a vector of values of the critical function.
Details
At most one of x, p, and alpha is allowed to be
a vector. Evaluates the critical function for the UMPU two-tailed
test for the binomial distribution, which satisfies the following
x <- seq(0, n)
phix <- umpu.binom(x, n, p, alpha)
px <- dbinom(x, n, p)
sum(phix * px) == alpha
sum(x * phix * px) == n * p * alpha