AverageStatisticEpistemicTest {FuzzySimRes}

Apply averaging statistics epistemic test for one or two fuzzy samples.

Description

'AverageStatisticEpistemicTest' calculates the p-value for the given real-valued statistical test using the averaging statistics epistemic bootstrap approach.

Usage

AverageStatisticEpistemicTest(
  sample1,
  sample2,
  bootstrapMethod = "std",
  test = "ks.test",
  cutsNumber = 1,
  criticalValueFunction = "KSTestCriticalValue",
  ...
)

Arguments

sample1

Sample of fuzzy numbers given in the form of a list or as a single number.

sample2

Sample of fuzzy numbers given in the form of a list or as a single number (two-sample test case) or NULL (one-sample test case).

bootstrapMethod

The standard (std) or antithetic (anti) method used for the epistemic bootstrap.

test

Name of the invoked function for the statistical test.

cutsNumber

Number of cuts used in the epistemic bootstrap.

criticalValueFunction

Name of the function that converts the test statistic into the p-value.

...

Additional arguments passed to the statistical test.

Details

The procedure calculates the p-value for the selected real-valued statistical test, like, e.g. the Kolmogorov-Smirnov one- or two-sample test (invoked by ks.test function). Another statistical test can be also used if it has at least one or two parameters (x for one or x,y for two real-valued samples, namely) and gives a list of at least two values (statistic for the output test statistic, and p.value for the calculated p-value). If necessary, the respective wrapper can be applied for the user-defined function. To choose the one-sample variant of the test, sample2=NULL should be used. Additional parameters to the statistical test can be passed with ...

As two input samples (sample1 and sample2, respectively), two lists of fuzzy numbers should be provided. These values have to be the fuzzy numbers defined in the FuzzyNumbers package (triangular, trapezoidal, etc.). If only one-sample test is used, sample1 is related to the fuzzy statistical sample, and sample2=NULL should be set.

Additionally, the function that calculates the p-value for the given critical level (i.e. value of the test statistic) should be provided using the parameter criticalValueFunction. This function is invoked with tree parameters: criticalValue - the critical value, n1 - tge size of the first initial sample, n2 - the size of the second initial sample (if necessary, otherwise n2=NA). For convenience, its variant for the Kolmogorov-Smirnov two-sample test is provided (the function KSTestCriticalValue).

To calculate the output, the averaging statistics epistemic bootstrap approach is used. Depending on the parameter bootstrapMethod, the standard (std) or antithetic (anti) method can be used. Then, the obtained test statistics are averaged to give the respective p-value and final result.

Value

The output is given in the form of a real number (the p-value) for the selected statistical test.

References

Grzegorzewski, P., Romaniuk, M. (2022) Bootstrap Methods for Epistemic Fuzzy Data. International Journal of Applied Mathematics and Computer Science, 32(2)

Grzegorzewski, P., Romaniuk, M. (2022) Bootstrapped Kolmogorov-Smirnov Test for Epistemic Fuzzy Data. Communications in Computer and Information Science, CCIS 1602, pp. 494-507, Springer

Gagolewski, M., Caha, J. (2021) FuzzyNumbers Package: Tools to deal with fuzzy numbers in R. R package version 0.4-7, https://cran.r-project.org/web/packages=FuzzyNumbers

See Also

MultiStatisticEpistemicTest for the epistemic bootstrap test related to multi-statistic approach, ResamplingStatisticEpistemicTest for the epistemic bootstrap test related to resampling statistics, EpistemicTest for the general epistemic bootstrap test

Other epistemic bootstrap statistical test: EpistemicTest(), MultiStatisticEpistemicTest(), ResamplingStatisticEpistemicTest()

Examples

# seed PRNG

set.seed(1234)

# generate two independent initial fuzzy samples

list1<-SimulateSample(20,originalPD="rnorm",parOriginalPD=list(mean=0,sd=1),
incrCorePD="rexp", parIncrCorePD=list(rate=2),
suppLeftPD="runif",parSuppLeftPD=list(min=0,max=0.6),
suppRightPD="runif", parSuppRightPD=list(min=0,max=0.6),
type="trapezoidal")


list2<-SimulateSample(20,originalPD="rnorm",parOriginalPD=list(mean=0,sd=1),
incrCorePD="rexp", parIncrCorePD=list(rate=2),
suppLeftPD="runif",parSuppLeftPD=list(min=0,max=0.6),
suppRightPD="runif", parSuppRightPD=list(min=0,max=0.6),
type="trapezoidal")

# apply the Kolmogorov-Smirnov two sample test for two different samples

AverageStatisticEpistemicTest(list1$value,list2$value,cutsNumber = 30)

# and the same sample twice

AverageStatisticEpistemicTest(list1$value,list1$value,cutsNumber = 30,bootstrapMethod = "anti")