# pokertest: the Poker test In randtoolbox: Toolbox for Pseudo and Quasi Random Number Generation and RNG Tests

## Description

The Poker test for testing random number generators.

## Usage

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

## 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`.

## Details

We consider a vector `u`, realisation of i.i.d. uniform random variables U1... Un.

Let us note k the card number (i.e. `nbcard`). The poker test computes a serie of 'hands' in {0, ..., k-1} from the sample u_i = floor(u_i k) (`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 = 1/k^k * k! / (k-j)!) * S_k^j,

where S_k^j denotes the Stirling numbers of the second kind. Finally the chi-squared statistic is

S = ∑_{j=1}^k [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. (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.

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.
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```# (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) ```