`random.walk.tests(x, B = 64, Excursion = TRUE, Expansion = TRUE, Height = TRUE, alpha = 0.05)`

x

a matrix that includes random data in base-2 format. See details for further information.

B

the length of words (B-bit). See Details section.

Excursion

if

`TRUE`

, Random Walk Excursion test is applied.
Expansion

if

`TRUE`

, Random Walk Expansion test is applied.
Height

if

`TRUE`

, Random Walk Height test is applied.
alpha

a predetermined value of significance level with the default value of 0.05.

- AD.statistic.Excursion
- value of test statistic of Anderson-Darling goodness-of-fit test conducted after application of Random Walk Excursion procedure.
- KS.statistic.Excursion
- value of test statistic of Kolmogorov-Smirnov goodness-of-fit test conducted after application of Random Walk Excursion procedure.
- CS.statistic.Excursion
- value of test statistic of Chi-Square goodness-of-fit test conducted after application of Random Walk Excursion procedure.
- AD.pvalue.Excursion
- p-value of Anderson-Darling goodness-of-fit test conducted after application of Random Walk Excursion procedure.
- KS.pvalue.Excursion
- p-value of Kolmogorov-Smirnov goodness-of-fit test conducted after application of Random Walk Excursion procedure.
- CS.pvalue.Excursion
- p-value of Chi-Square goodness-of-fit test conducted after application of Random Walk Excursion procedure.
- AD.result.Excursion
- returns 0 if H0 is rejected and 1 otherwise in Anderson-Darling goodness-of-fit test conducted after application of Random Walk Excursion procedure.
- KS.result.Excursion
- returns 0 if H0 is rejected and 1 otherwise in Kolmogorov-Smirnov goodness-of-fit test conducted after application of Random Walk Excursion procedure.
- CS.result.Excursion
- returns 0 if H0 is rejected and 1 otherwise in Chi-Square goodness-of-fit test conducted after application of Random Walk Excursion procedure.
- AD.statistic.Expansion
- value of test statistic of Anderson-Darling goodness-of-fit test conducted after application of Random Walk Expansion procedure.
- KS.statistic.Expansion
- value of test statistic of Kolmogorov-Smirnov goodness-of-fit test conducted after application of Random Walk Expansion procedure.
- CS.statistic.Expansion
- value of test statistic of Chi-Square goodness-of-fit test conducted after application of Random Walk Expansion procedure.
- AD.pvalue.Expansion
- p-value of Anderson-Darling goodness-of-fit test conducted after application of Random Walk Expansion procedure.
- KS.pvalue.Expansion
- p-value of Kolmogorov-Smirnov goodness-of-fit test conducted after application of Random Walk Expansion procedure.
- CS.pvalue.Expansion
- p-value of Chi-Square goodness-of-fit test conducted after application of Random Walk Expansion procedure.
- AD.result.Expansion
- returns 0 if H0 is rejected and 1 otherwise in Anderson-Darling goodness-of-fit test conducted after application of Random Walk Expansion procedure.
- KS.result.Expansion
- returns 0 if H0 is rejected and 1 otherwise in Kolmogorov-Smirnov goodness-of-fit test conducted after application of Random Walk Expansion procedure.
- CS.result.Expansion
- returns 0 if H0 is rejected and 1 otherwise in Chi-Square goodness-of-fit test conducted after application of Random Walk Expansion procedure.
- AD.statistic.Height
- value of test statistic of Anderson-Darling goodness-of-fit test conducted after application of Random Walk Height procedure.
- KS.statistic.Height
- value of test statistic of Kolmogorov-Smirnov goodness-of-fit test conducted after application of Random Walk Height procedure.
- CS.statistic.Height
- value of test statistic of Chi-Square goodness-of-fit test conducted after application of Random Walk Height procedure.
- AD.pvalue.Height
- p-value of Anderson-Darling goodness-of-fit test conducted after application of Random Walk Height procedure.
- KS.pvalue.Height
- p-value of Kolmogorov-Smirnov goodness-of-fit test conducted after application of Random Walk Height procedure.
- CS.pvalue.Height
- p-value of Chi-Square goodness-of-fit test conducted after application of Random Walk Height procedure.
- AD.result.Height
- returns 0 if H0 is rejected and 1 otherwise in Anderson-Darling goodness-of-fit test conducted after application of Random Walk Height procedure.
- KS.result.Height
- returns 0 if H0 is rejected and 1 otherwise in Kolmogorov-Smirnov goodness-of-fit test conducted after application of Random Walk Height procedure.
- CS.result.Height
- returns 0 if H0 is rejected and 1 otherwise in Chi-Square goodness-of-fit test conducted after application of Random Walk Height procedure.

`x`

should be entered as a matrix of bits of dimension $B$x$k$, where $k$ is the number of words (integers) generated by the RNG of interest.If `Excursion`

is TRUE, B takes the values 16, 32, 64, 128, and 256. If `Height`

is TRUE, B takes 64, 128, 256, 512, and 1024. If `Expansion`

is TRUE, B takes 32, 64, and 128. Because theoretical cumulative distribution functions for the other word lengths, `random.walk.tests()`

performs tests under given bit settings. If one of the tests is not applied, all the results related with that test in output are set to -1.

```
RNGkind(kind = "Super-Duper")
B=64 # Bit length is 64.
k=500 # Generate 500 integers.
dat=round(runif(k,0,(2^B-1)))
x=sfsmisc::digitsBase(dat, base= 2, B) #Convert to base 2
alpha = 0.05
test=random.walk.tests(x, B, Excursion = TRUE, Expansion = TRUE, Height = TRUE, alpha)
print(test)
```

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