order.test | R Documentation |
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. 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
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.
# (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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