EpistemicCorrectedVariance {FuzzySimRes}

Calculate the corrected variance using the epistemic bootstrap.

Description

'EpistemicCorrectedVariance' calculates the corrected estimator of the variance for the fuzzy sample using the epistemic bootstrap approach.

Usage

EpistemicCorrectedVariance(
  fuzzySample,
  cutsNumber = 1,
  bootstrapMethod = "std",
  ...
)

Arguments

fuzzySample

Sample of fuzzy numbers (given in the form of a list or as a single number) or a matrix with already sampled values (i.e. output of function AntitheticBootstrap or EpistemicBootstrap).

cutsNumber

Number of cuts used in the epistemic bootstrap.

bootstrapMethod

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

...

Possible parameters passed to other functions.

Details

For the initial sample given by fuzzySample, the function calculates the corrected estimator of the variance using the standard (if bootstrapMethod is set to "std") or the antithetic (when bootstrapMethod="anti") epistemic bootstrap. The initial sample should be given in the form of a list of numbers or a single number. These values have to be the fuzzy numbers defined in the FuzzyNumbers package. The corrected estimator of the variance separates the within- and between-group variations. For the details, see (Grzegorzewski, Romaniuk, 2022a).

If, instead of fuzzy sample, the matrix is given by the parameter fuzzySample, then this matrix is treated as the direct output from the epistemic or the antithetic bootstrap. Then, the corrected estimator of the variance is directly calculated.

Value

The output is given in the form of a real number (the estimator of the variance).

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

EpistemicMean for the epistemic estimator of the mean, EpistemicEstimator for the general function concerning the epistemic estimator calculation

Other epistemic estimators: EpistemicMean()

Examples

# seed PRNG

set.seed(1234)

# generate an initial fuzzy sample

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")



# calculate the corrected variance using the standard epistemic bootstrap approach

EpistemicCorrectedVariance(list1$value,cutsNumber = 30)

# calculate the corrected variance using the antithetic epistemic bootstrap approach

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

# use the epistemic bootstrap

list1Epistemic<-EpistemicBootstrap(list1$value,cutsNumber = 10)

# calculate the standard deviation using the obtained output

EpistemicCorrectedVariance(list1Epistemic)