EpistemicMean {FuzzySimRes}

Estimate the mean using the epistemic bootstrap.

Description

'EpistemicMean' calculates the mean of the fuzzy sample using the epistemic bootstrap approach.

Usage

EpistemicMean(
  fuzzySample,
  cutsNumber = 1,
  bootstrapMethod = "std",
  trueValue = NA
)

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.

trueValue

The true (usually unknown) value of the estimated parameter. If NA is used for this parameter, the SE is calculated.

Details

For the initial sample given by fuzzySample, the function estimates its mean 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.

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 mean is directly calculated.

Additionally, the standard error (SE) of this estimator is calculated and its mean squared error (MSE). This second type of the error is used if some value (other than NA) is provided for the trueValue parameter.

Value

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

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

EpistemicEstimator for the general function concerning the epistemic estimator calculation, EpistemicCorrectedVariance for the corrected epistemic estimator of the variance

Other epistemic estimators: EpistemicCorrectedVariance()

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 mean using the standard epistemic bootstrap approach

EpistemicMean(list1$value,cutsNumber = 30)

# calculate the mean using the antithetic epistemic bootstrap approach

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