randtoolbox (version 2.0.2)

order.test: the Order test

Description

The Order test for testing random number generators.

Usage

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

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).

Arguments

u

sample of random numbers in ]0,1[.

echo

logical to plot detailed results, default TRUE

d

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

Author

Christophe Dutang.

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. \(x<y<z\), \(x<z<y\), \(y<x<z\), \(y<z<x\), \(z<x<y\) and \(z<y<x\). The Marsaglia test computes the empirical of the different permutations as well as the theoretical one \(n/6\) where \(n\) is the number of triplets. Finally the chi-squared statistic is $$ S = \sum_{j=0}^{6} \frac{n_j - n/6)^2}{n/6}. $$

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.

See Also

other tests of this package freq.test, serial.test, poker.test, gap.test and coll.test

ks.test for the Kolmogorov Smirnov test and acf for the autocorrelation function.

Examples

# (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)