sherman.unif.test: Sherman test for uniformity

Description Usage Arguments Details Value Author(s) References Examples

Description

Performs Sherman test for the hypothesis of uniformity, see Sherman (1950).

Usage

1
sherman.unif.test(x, nrepl=2000)

Arguments

x

a numeric vector of data values.

nrepl

the number of replications in Monte Carlo simulation.

Details

The Sherman test for uniformity is based on the following statistic:

B_n = \frac{1}{2}∑_{i=1}^{n+1}{≤ft| X_{(i)} - X_{(i-1)} - \frac{1}{n+1} \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 Sherman statistic.

p.value

the p-value for the test.

method

the character string "Sherman test for uniformity".

data.name

a character string giving the name(s) of the data.

Author(s)

Maxim Melnik and Ruslan Pusev

References

Sherman, B. (1950): A random variable related to the spacing of sample values. — Ann. Math. Stat., vol. 21, pp. 339–361.

Examples

1
2

Example output

Loading required package: orthopolynom
Loading required package: polynom

	Sherman test for uniformity

data:  runif(100, 0, 1)
W = 0.32762, p-value = 0.955


	Sherman test for uniformity

data:  runif(100, 0.1, 0.9)
W = 0.41253, p-value = 0.0285

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