quesenberry.unif.test: Quesenberry--Miller test 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.
Value
A list with class "htest" containing the following components:
statisticthe value of the Quesenberry--Miller statistic.
p.valuethe p-value for the test.
methodthe character string "Quesenberry--Miller test for uniformity".
data.namea character string giving the name(s) of the data.
Details
The Quesenberry--Miller test for uniformity is based on the following statistic:
$$B_n = \sum_{i=1}^{n+1}{\left( X_{(i)} - X_{(i-1)} \right)^2} + \sum_{i=1}^{n}{\left( X_{(i)} - X_{(i-1)} \right)\left( X_{(i+1)} - X_{(i)} \right)},$$
where $X_{(0)}=0$, $X_{(n+1)}=1$.
The p-value is computed by Monte Carlo simulation.
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.