| gap.test {randtoolbox} | R Documentation |
the Gap test
Description
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 |
upper |
numeric for the upper bound, default |
echo |
logical to plot detailed results, default |
Details
We consider a vector u, realisation of i.i.d. uniform random
variables U_1, \dots, U_n.
The gap test works on the 'gap' variables defined as
G_ i =
\left\{
\begin{array}{cl}
1 & \textrm{if~} lower \leq U_i \leq upper\\
0 & \textrm{otherwise}\\
\end{array}
\right.
Let p the probability that G_i equals to one.
Then we compute the length of zero gaps and denote by n_j the number
of zero gaps of length j. The chi-squared statistic is given by
S = \sum_{j=1}^m \frac{(n_j - n p_j)^2}{n p_j},
where p_j 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
\left\lfloor \frac{ \log( 10^{-1} ) - 2\log(1- p)-log(n) }{ \log( p )} \right\rfloor
).
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. 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
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.
Examples
# (1)
#
gap.test(runif(1000))
print( gap.test( runif(1000000), echo=FALSE ) )
# (2)
#
gap.test(runif(1000), 1/3, 2/3)