the Frequency test
The Frequency test for testing random number generators.
freq.test(u, seq = 0:15, echo = TRUE)
u |
sample of random numbers in ]0,1[. |
echo |
logical to plot detailed results, default |
seq |
a vector of contiguous integers, default |
We consider a vector u, realisation of i.i.d. uniform random
variables U1... Un.
The frequency test works on a serie seq of ordered contiguous integers
(s_1, ...,s_d), where s_j in Z. From the
sample u, we compute observed integers as
d_i = floor( u_i * ( s_d + 1 ) + s_1 ),
(i.e. d_i are uniformely distributed in {s_1, ...,s_d}). The expected number of integers equals to j is m=n/(s_d - s_1+1). Finally, the chi-squared statistic is
S = ∑_{j=1}^d (card(d_i=s_j) - m)^2/m .
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. (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.
other tests of this package gap.test, serial.test, poker.test,
order.test and coll.test
# (1) # freq.test(runif(1000)) print( freq.test( runif(1000000), echo=FALSE) ) # (2) # freq.test(runif(1000), 1:4) freq.test(runif(1000), 10:40)
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