The Gap test for testing random number generators.
Usage
gap.test(u, lower = 0, upper = 1/2, echo = TRUE)
Arguments
u
sample of random numbers in ]0,1[.
lower
numeric for the lower bound, default 0.
upper
numeric for the upper bound, default 1/2.
echo
logical to plot detailed results, default TRUE
Details
We consider a vector u, realisation of i.i.d. uniform random
variables U1... Un.
The gap test works on the 'gap' variables defined as
1 if lower <= Ui <= upper, 0 otherwise.
Let p the probability that Gi equals to one.
Then we compute the length of zero gaps and denote by nj the number
of zero gaps of length j. The chi-squared statistic is given by
S = ∑_{j=0}^m (n_j - n p_j)^2/[n p_j],
where pj stands for the probability the length of zero gaps equals
to j (
(1-p)^2 p^j
) and m the max number of lengths (at least
floor( ( log( 10^(-1) ) - 2log( 1-p )-log(n) ) / log( p ) ).
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, poker.test,
order.test and coll.test
ks.test for the Kolmogorov Smirnov test and acf for
the autocorrelation function.