serialtest: the Serial test

In randtoolbox: Toolbox for Pseudo and Quasi Random Number Generation and Random Generator Tests

the Serial test

Description

The Serial test for testing random number generators.

Usage

serial.test(u , d = 8, echo = TRUE)

Arguments

u	sample of random numbers in ]0,1[.
echo	logical to plot detailed results, default TRUE
d	a numeric for the dimension, see details. When necessary we assume that d is a multiple of the length of u.

Details

We consider a vector u, realisation of i.i.d. uniform random variables U_1, \dots, U_n.

The serial test computes a serie of integer pairs (p_i,p_{i+1}) from the sample u with p_i = \lfloor u_i d\rfloor (u must have an even length). Let n_j be the number of pairs such that j=p_i \times d + p_{i+1}. If d=2, we count the number of pairs equals to 00, 01, 10 and 11. Since all the combination of two elements in \{0, \dots, d-1\} are equiprobable, the chi-squared statistic is

S = \sum_{j=0}^{d-1} \frac{n_j - n/(2 d^2))^2}{n/(2 d^2)}.

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1145/1268776.1268777")}

See Also

other tests of this package freq.test, gap.test, poker.test, order.test and coll.test

ks.test for the Kolmogorov Smirnov test and acf for the autocorrelation function.

Examples

# (1) 
#
serial.test(runif(1000))
print( serial.test( runif(1000000), d=2, e=FALSE) )

# (2) 
#
serial.test(runif(5000), 5) 

randtoolbox documentation built on Oct. 18, 2024, 5:13 p.m.