| poker.test {randtoolbox} | R Documentation |
the Poker test
Description
The Poker test for testing random number generators.
Usage
poker.test(u , nbcard = 5, echo = TRUE)
Arguments
u |
sample of random numbers in ]0,1[. |
echo |
logical to plot detailed results, default |
nbcard |
a numeric for the number of cards,
we assume that the length of |
Details
We consider a vector u, realisation of i.i.d. uniform random
variables U_1, \dots, U_n.
Let us note k the card number (i.e. nbcard).
The poker test computes a serie of 'hands' in \{0, \dots, k-1\}
from the sample h_i = \lfloor u_i d\rfloor (u must have a length dividable by k). Let
n_j be the number of 'hands' with (exactly) j different cards. The
probability is
p_j = \frac{k!}{k^k (k-j)!* S_k^j}
* (\frac{j}{k})^(k-j),
where S_k^j denotes the Stirling numbers of the second kind. Finally the
chi-squared statistic is
S = \sum_{j=0}^{k-1} \frac{n_j - np_j/k)^2}{np_j/k}.
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, serial.test, gap.test,
order.test and coll.test
ks.test for the Kolmogorov Smirnov test and acf for
the autocorrelation function.
Examples
# (1) hands of 5 'cards'
#
poker.test(runif(50000))
# (2) hands of 4 'cards'
#
poker.test(runif(40000), 4)
# (3) hands of 42 'cards'
#
poker.test(runif(420000), 42)