order.test: the Order test

Description

The Order test for testing random number generators.

Usage

order.test(u, d = 3, echo = TRUE)

Arguments

sample of random numbers in ]0,1[.

echo

logical to plot detailed results, default TRUE

a numeric for the dimension, see details. When necessary we assume that d is a multiple of the length of u.

Value

a list with the following components :
statistic the value of the chi-squared statistic.
p.value the p-value of the test.
observed the observed counts.
expected the expected counts under the null hypothesis.
residuals the Pearson residuals, (observed - expected) / sqrt(expected).

Details

We consider a vector u, realisation of i.i.d. uniform random variables $U_1, \dots, U_n$.

The Order test works on a sequence of d-uplets ($x,y,z$ when d=3) of uniform i.i.d. random variables. The triplet is build from the vector $u$. The number of permutation among the components of a triplet is $3!=6$, i.e. $x

References

Planchet F., Jacquemin J. (2003), L'utilisation de methodes de simulation en assurance. Bulletin Francais d'Actuariat, vol. 6, 11, 3-69. (available online)

L'Ecuyer P. (2001), Software for uniform random number generation distinguishing the good and the bad. Proceedings of the 2001 Winter Simulation Conference. (available online)

L'Ecuyer P. (2007), Test U01: a C library for empirical testing of random number generators. ACM Trans. on Mathematical Software 33(4), 22.

Examples

Run this code

# (1) mersenne twister vs torus
#
order.test(runif(6000))
order.test(torus(6000))

# (2) 
#
order.test(runif(4000), 4)
order.test(torus(4000), 4)

# (3) 
#
order.test(runif(5000), 5)
order.test(torus(5000), 5)

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