| coll.test.sparse {randtoolbox} | R Documentation |
the Collision test
Description
The Collision test for testing random number generators.
Usage
coll.test.sparse(rand, lenSample = 2^14, segments = 2^10, tdim = 2,
nbSample = 10, ...)
Arguments
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 number of repetitions of the test. |
... |
further arguments to pass to function rand |
Details
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).
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) = \prod_{i=0}^{n-c-1}\frac{k-i}{k} \frac{1}{k^c} {}_2S_n^{n-c},
where {}_2S_n^k denotes the Stirling number of the second kind
and c=0,\dots,n-1.
This formula cannot be used for large n since the Stirling number
need O(n\log(n)) time to be computed. We use
a Poisson approximation if \frac{n}{k} < \frac{1}{32} and
the exact formula otherwise.
The test is repeated nbSample times and the result of each
repetition forms a row in the output table.
Value
A data frame with nbSample rows and the following columns.
observed the observed counts.
p.value the p-value of the test.
Author(s)
Christophe Dutang, Petr Savicky.
References
P. L'Ecuyer, R. Simard, S. Wegenkittl, Sparse serial tests of uniformity for random number generators. SIAM Journal on Scientific Computing, 24, 2 (2002), 652-668. doi:10.1137/S1064827598349033
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 coll.test, freq.test, serial.test, poker.test,
order.test and gap.test
ks.test for the Kolmogorov Smirnov test and acf for
the autocorrelation function.
Examples
# (1) poisson approximation
#
coll.test.sparse(runif)
# (2) exact distribution
#
coll.test.sparse(SFMT, lenSample=2^7, segments=2^5, tdim=2, nbSample=10)
## Not run:
#A generator with too uniform distribution (too small number of collisions)
#produces p-values close to 1
set.generator(name="congruRand", mod="2147483647", mult="742938285", incr="0", seed=1)
coll.test.sparse(runif, lenSample=300000, segments=50000, tdim=2)
#Park-Miller generator has too many collisions and produces small p-values
set.generator(name="congruRand", mod="2147483647", mult="16807", incr="0", seed=1)
coll.test.sparse(runif, lenSample=300000, segments=50000, tdim=2)
## End(Not run)