| serial.test {randtoolbox} | R Documentation |
the Serial test
Description
The Serial test for testing random number generators.
Usage
serial.test(u , d = 8, echo = TRUE)
Arguments
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 |
Details
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)}.
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, gap.test, poker.test,
order.test and coll.test
ks.test for the Kolmogorov Smirnov test and acf for
the autocorrelation function.
Examples
# (1)
#
serial.test(runif(1000))
print( serial.test( runif(1000000), d=2, e=FALSE) )
# (2)
#
serial.test(runif(5000), 5)