CryptRndTest (version 1.2.2)

TBT.criticalValue: Critical value for Topological Binary Test

Description

Approximately computes cumulative distribution function of the test statistic of the Topological Binary Test of Alcover et al. (2013) and finds the required critical value for the test.

Usage

TBT.criticalValue(m, k, alpha = 0.01, cdf = FALSE, exact = TRUE)

Arguments

m

the length of words (B-bit) in Topological Binary Test.

k

the number of words (integers) generated by the RNG of interest that will be tested.

alpha

a predetermined value of type-I error with the default value of 0.05.

cdf

if TRUE, the cumulative distribution function of the test statistic is stored and printed.

exact

if TRUE, the function Stirling2 from the package gmp is used to calculate the Stirling numbers of the second kind in the case that the function Strlng2 from the package CryptRndTest returns a NaN. Otherwise, nothing is done for NaN's generated by Strlng2.

Value

prob

a vector containing the cumulative probabilities corresponding to the values in value.

value

a vector containing the values of the test statistic.

critical.value

critical value of the test statistic corresponding to alpha.

Details

The function TBT.criticalValue lists the cumulative probabilities greater than zero if cdf is set to TRUE.

A correction factor is applied to improve accuracy of the the function Strlng2 in the computation of probabilities. Accuracy of the computations decreases with increasing value of m.

References

Alcover, P.M., Guillamon, A., Ruiz, M.C., A new randomness test for bit sequences. Informatica (2013), 24(3), 339--356.

Examples

# Critical values for the Topological Binary Test at 0.01 and 0.05 levels of significance.

TBT.criticalValue(m=8, k=256, alpha=0.01, cdf=FALSE, exact=FALSE)
TBT.criticalValue(m=8, k=256, alpha=0.05, cdf=FALSE, exact=FALSE)