Performs Sherman test for the hypothesis of uniformity,
see Sherman (1950).
Usage
sherman.unif.test(x, nrepl=2000)
Arguments
x
a numeric vector of data values.
nrepl
the number of replications in Monte Carlo simulation.
Value
A list with class "htest" containing the following components:
statisticthe value of the Sherman statistic.
p.valuethe p-value for the test.
methodthe character string "Sherman test for uniformity".
data.namea character string giving the name(s) of the data.
Details
The Sherman test for uniformity is based on the following statistic:
$$B_n = \frac{1}{2}\sum_{i=1}^{n+1}{\left| X_{(i)} - X_{(i-1)} - \frac{1}{n+1} \right|},$$
where $X_{(0)}=0$, $X_{(n+1)}=1$.
The p-value is computed by Monte Carlo simulation.
References
Sherman, B. (1950): A random variable related to the spacing of sample values. --- Ann. Math. Stat., vol. 21, pp. 339--361.