coll.test | R Documentation |
The Collision test for testing random number generators.
coll.test(rand, lenSample = 2^14, segments = 2^10, tdim = 2, nbSample = 1000, echo = TRUE, ...)
rand |
a function generating random numbers. its first argument must be
the 'number of observation' argument as in |
lenSample |
numeric for the length of generated samples. |
segments |
numeric for the number of segments to which the interval |
tdim |
numeric for the length of the disjoint t-tuples. |
nbSample |
numeric for the overall sample number. |
echo |
logical to plot detailed results, default |
... |
further arguments to pass to function rand |
We consider outputs of multiple calls to a random number generator rand
.
Let us denote by n the length of samples (i.e. lenSample
argument),
k the number of cells (i.e. nbCell
argument) and
m the number of samples (i.e. nbSample
argument).
A collision is defined as when a random number falls in a cell where there are already random numbers. Let us note C the number of collisions
The distribution of collision number C is given by
P(C = c) = ∏_{i=0}^{n-c-1} (k-i)/k *1/(k^c) 2S_n^{n-c},
where 2S_n^{n-c} denotes the Stirling number of the second kind and c=0,..., n-1.
But we cannot use this formula for large n since the Stirling number need O(n log(n)) time to be computed. We use a Gaussian approximation if n/k>\frac{1}{32} and n >= 2^8, a Poisson approximation if n/k < 1/32 and the exact formula otherwise.
Finally we compute m samples of random numbers, on which we calculate the number of collisions. Then we are able to compute a chi-squared statistic.
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).
Christophe Dutang.
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
other tests of this package coll.test.sparse
, freq.test
, serial.test
, poker.test
,
order.test
and gap.test
ks.test
for the Kolmogorov Smirnov test and acf
for
the autocorrelation function.
# (1) poisson approximation # coll.test(runif, 2^7, 2^10, 1, 100) # (2) exact distribution # coll.test(SFMT, 2^7, 2^10, 1, 100)
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