umpu.binom: UMPU Test for the Binomial Distribution

In ump: Uniformly Most Powerful Tests

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.

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
  

when p is strictly between zero and one.

Value

a vector of values of the critical function.

Examples

library(ump)
umpu.binom(0:10, 10, 0.6, 0.1)

Example output

 [1] 1.00000000 1.00000000 1.00000000 0.83289497 0.00000000 0.00000000
 [7] 0.00000000 0.00000000 0.04942615 1.00000000 1.00000000

ump documentation built on May 1, 2019, 11:10 p.m.