randtoolbox (version 2.0.2)

poker.test: the Poker test

Description

The Poker test for testing random number generators.

Usage

poker.test(u , nbcard = 5, echo = TRUE)

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).

Arguments

u

sample of random numbers in ]0,1[.

echo

logical to plot detailed results, default TRUE

nbcard

a numeric for the number of cards, we assume that the length of u is a multiple of nbcard.

Author

Christophe Dutang.

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 $$ S = \sum_{j=0}^{k-1} \frac{n_j - np_j/k)^2}{np_j/k}. $$

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. (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.

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)