the Order test
The Order test for testing random number generators.
order.test(u, d = 3, echo = TRUE)
u |
sample of random numbers in ]0,1[. |
echo |
logical to plot detailed results, default |
d |
a numeric for the dimension, see details. When necessary
we assume that |
We consider a vector u, realisation of i.i.d. uniform random
variables U1... Un.
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 = ∑_{j=1}^6 [n_j - n/6 ]^2/[n/6].
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).
Christophe Dutang.
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.
other tests of this package freq.test, serial.test, poker.test,
gap.test and coll.test
# (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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