gap.test | R Documentation |
The Gap test for testing random number generators.
gap.test(u, lower = 0, upper = 1/2, echo = TRUE)
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 |
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 ) ).
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. 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
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.
# (1) # gap.test(runif(1000)) print( gap.test( runif(1000000), echo=FALSE ) ) # (2) # gap.test(runif(1000), 1/3, 2/3)
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