quesenberry.unif.test: Quesenberry-Miller test for uniformity

In uniftest: Tests for Uniformity

Description

Performs Quesenberry–Miller test for the hypothesis of uniformity, see Quesenberry and Miller (1977).

Usage

quesenberry.unif.test(x, nrepl=2000)

Arguments

x	a numeric vector of data values.

nrepl

the number of replications in Monte Carlo simulation.

Details

The Quesenberry–Miller test for uniformity is based on the following statistic:

B_n = ∑_{i=1}^{n+1}{≤ft( X_{(i)} - X_{(i-1)} \right)^2} + ∑_{i=1}^{n}{≤ft( X_{(i)} - X_{(i-1)} \right)≤ft( X_{(i+1)} - X_{(i)} \right)},

where X_{(0)}=0, X_{(n+1)}=1. The p-value is computed by Monte Carlo simulation.

Value

A list with class "htest" containing the following components:

statistic	the value of the Quesenberry–Miller statistic.
p.value	the p-value for the test.
method	the character string "Quesenberry–Miller test for uniformity".
data.name	a character string giving the name(s) of the data.

Author(s)

Maxim Melnik and Ruslan Pusev

References

Quesenberry, C.P. and Miller F.L. (1977): Power studies of some tests for uniformity. — J. Stat. Comput. Simul., vol. 5, pp. 169–191.

Examples

quesenberry.unif.test(runif(100,0,1))
quesenberry.unif.test(runif(100,0,1.05))

Example output

Loading required package: orthopolynom
Loading required package: polynom

	Greenwood-Quesenberry-Miller test for uniformity

data:  runif(100, 0, 1)
Q = 0.030136, p-value = 0.291


	Greenwood-Quesenberry-Miller test for uniformity

data:  runif(100, 0, 1.05)
Q = 0.03507, p-value = 0.015

uniftest documentation built on May 1, 2019, 7:33 p.m.