serial.test | R Documentation |
The Serial test for testing random number generators.
serial.test(u , d = 8, 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 serial test computes a serie of integer pairs (p_i,p_{i+1})
from the sample u
with
p_i = floor(u_i d) (u
must have an even length).
Let n_j be the number of pairs such that
j=p_i d + p_{i+1}. If d=2
, we count
the number of pairs equals to 00, 01, 10 and 11. Since
all the combination of two elements in {0, ..., d-1}
are equiprobable, the chi-squared statistic is
S = ∑_{j=0}^{d-1} [n_j - n/(2 d^2)]^2/[n/(2 d^2)].
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
, gap.test
, poker.test
,
order.test
and coll.test
ks.test
for the Kolmogorov Smirnov test and acf
for
the autocorrelation function.
# (1) # serial.test(runif(1000)) print( serial.test( runif(1000000), d=2, e=FALSE) ) # (2) # serial.test(runif(5000), 5)
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