| freq.test {randtoolbox} | R Documentation |
the Frequency test
Description
The Frequency test for testing random number generators.
Usage
freq.test(u, seq = 0:15, echo = TRUE)
Arguments
u |
sample of random numbers in ]0,1[. |
echo |
logical to plot detailed results, default |
seq |
a vector of contiguous integers, default |
Details
We consider a vector u, realisation of i.i.d. uniform random
variables U_1, \dots, U_n.
The frequency test works on a serie seq of ordered contiguous integers
(s_1,\dots,s_d), where s_j\in Z\!\!Z. From the
sample u, we compute observed integers as
d_i = \lfloor u_i * ( s_d + 1 ) + s_1 \rfloor,
(i.e. d_i are uniformely distributed in
\{s_1,\dots,s_d\}). The expected number of integers equals to
j is m= \frac{1}{s_d - s_1+1}\times n. Finally, the
chi-squared statistic is
S = \sum_{j=1}^d \frac{(card(d_i=s_j) - m)^2}{m}.
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 gap.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)
#
freq.test(runif(1000))
print( freq.test( runif(10000), echo=FALSE) )
# (2)
#
freq.test(runif(1000), 1:4)
freq.test(runif(1000), 10:40)