order.test {randtoolbox}

the Order test

Description

The Order test for testing random number generators.

Usage

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

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.

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}.

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).

Author(s)

Christophe Dutang.

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. doi:10.1109/WSC.2001.977250

L'Ecuyer P. (2007), Test U01: a C library for empirical testing of random number generators. ACM Trans. on Mathematical Software 33(4), 22. doi:10.1145/1268776.1268777

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)