The Serial test for testing random number generators.
serial.test(u , d = 8, echo = TRUE)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).
sample of random numbers in ]0,1[.
logical to plot detailed results, default TRUE
a numeric for the dimension, see details. When necessary
we assume that d is a multiple of the length of u.
Christophe Dutang.
We consider a vector u, realisation of i.i.d. uniform random
variables \(U_1, \dots, U_n\).
The serial test computes a serie of integer pairs \((p_i,p_{i+1})\)
from the sample u with \(p_i = \lfloor u_i d\rfloor\) (u must have an even length).
Let \(n_j\) be the number of pairs such that
\(j=p_i \times d + p_{i+1}\). If d=2, we count
the number of pairs equals to \(00, 01, 10\) and \(11\). Since
all the combination of two elements in \(\{0, \dots, d-1\}\)
are equiprobable, the chi-squared statistic is
$$ S = \sum_{j=0}^{d-1} \frac{n_j - n/(2 d^2))^2}{n/(2 d^2)}.
$$
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.
# (1)
#
serial.test(runif(1000))
print( serial.test( runif(1000000), d=2, e=FALSE) )
# (2)
#
serial.test(runif(5000), 5)
Run the code above in your browser using DataLab