# the Poker test

### 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 |

`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 *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.

### 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 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)
``` |

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