# sherman.unif.test: Sherman test for uniformity In uniftest: Tests for Uniformity

## 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 sherman.unif.test(runif(100,0,1)) sherman.unif.test(runif(100,0.1,0.9)) 

### Example output

Loading required package: orthopolynom

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.