The goal of FuzzySimRes, a library written in R, is to simulate synthetic fuzzy data and provide so-called epistemic bootstrap procedures.
The simulation procedures are useful to generate synthetic samples that can be applied in statistical inference (see, e.g., (P. Grzegorzewski, Hryniewicz, and Romaniuk 2020a, 2020b; Parchami, Grzegorzewski, and Romaniuk 2024)) and consist of fuzzy numbers (e.g., triangular or trapezoidal ones).
The epistemic bootstrap is used for epistemic fuzzy data (see (Couso and Dubois 2014)) and it allows (see (P. Grzegorzewski and Romaniuk 2021; Przemyslaw Grzegorzewski and Romaniuk 2022)):
Additionally, the special epistemic fuzzy real-life data set is provided (see (Faraz and Shapiro 2010)) which consists of triangular fuzzy numbers.
The fuzzy data used in this package should be defined as the variables introduced in (Gagolewski and Caha 2021) (as, e.g., triangular fuzzy numbers).
The following procedures are available in the library:
You can install the latest development version of FuzzyResampling with:
library(devtools)
install_github("mroman-ibs/FuzzySimRes")You can install the latest stable version from CRAN with:
install.packages("FuzzySimRes")# set seed
set.seed(12345)
# load library
library(FuzzySimRes)
# generate the initial sample consisting of 5 trapezoidal fuzzy numbers
sample1 <- SimulateSample(5,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 epistemic bootstrap with 10 cuts
EpistemicBootstrap (sample1$value, cutsNumber=10)
#> X1 X2 X3 X4 X5
#> 0.3616 1.1497756 1.892964 -0.4412416 -0.4123010 -0.21887696
#> 0.8688 1.0789047 2.256274 0.8043010 -0.2897991 0.21447852
#> 0.9042 1.0821638 1.558882 -0.5234141 -0.4201384 0.01919864
#> 0.6174 0.9770422 1.871995 0.2864493 -0.4820862 0.22506592
#> 0.134 1.4685182 1.471085 1.1883406 -0.7735033 -0.53509789
#> 0.7822 1.6920152 2.316149 0.3981874 -0.3132989 0.29258249
#> 0.4292 1.6567735 1.597893 0.1417311 -0.4820543 0.24728641
#> 0.9273 1.2565657 2.537325 -0.1589284 -0.6728166 -0.22298375
#> 0.7732 1.1521309 2.275875 -0.2135284 -0.7091520 0.07312683
#> 0.2597 1.5825929 2.525235 -0.8153841 -0.7529021 0.17019910
# apply the antithetic bootstrap with 10 cuts
AntitheticBootstrap (sample1$value, cutsNumber=10)
#> X1 X2 X3 X4 X5
#> 0.5138 1.715099 2.348629 0.84791420 -0.4155065 -0.10278774
#> 0.7201 1.657023 2.315396 0.75226172 -0.2950119 -0.18807131
#> 0.7499 1.525241 1.529150 0.04191831 -0.4140887 0.28010819
#> 0.0956 1.036562 1.548077 0.88263662 -0.2954918 -0.28473900
#> 0.3978 1.123620 2.289173 0.08373510 -0.4331157 -0.19568336
#> 0.2945 1.423709 1.622644 0.68312991 -0.4069346 0.13470515
#> 0.6173 1.300673 2.154367 0.27146818 -0.6049461 0.30957665
#> 0.9743 1.153848 1.880561 0.76471178 -0.5728187 -0.29215072
#> 0.6182 1.384238 2.107480 0.30352891 -0.6221601 -0.08907579
#> 0.5214 1.574392 1.977895 -0.28340154 -0.3810230 0.25160955
# calculate the mean using the standard epistemic bootstrap approach
EpistemicMean(sample1$value,cutsNumber = 30)
#> $value
#> [1] 0.60163
#>
#> $SE
#> [1] 0.1570901
#>
#> $MSE
#> [1] NA
# calculate the median using the antithetic epistemic bootstrap approach
EpistemicEstimator(sample1$value,estimator="median",cutsNumber = 30,bootstrapMethod="anti")
#> $value
#> [1] 0.136565
#>
#> $SE
#> [1] 0.2187421
#>
#> $MSE
#> [1] NA
# generate two independent initial fuzzy samples
list1<-SimulateSample(20,originalPD="rnorm",parOriginalPD=list(mean=0,sd=1),
incrCorePD="rexp", parIncrCorePD=list(rate=2),
suppLeftPD="runif",parSuppLeftPD=list(min=0,max=0.6),
suppRightPD="runif", parSuppRightPD=list(min=0,max=0.6),
type="trapezoidal")
list2<-SimulateSample(20,originalPD="rnorm",parOriginalPD=list(mean=0,sd=1),
incrCorePD="rexp", parIncrCorePD=list(rate=2),
suppLeftPD="runif",parSuppLeftPD=list(min=0,max=0.6),
suppRightPD="runif", parSuppRightPD=list(min=0,max=0.6),
type="trapezoidal")
# apply the Kolmogorov-Smirnov two-sample test for two different samples
# with the average statistics approach
EpistemicTest(list1$value,list2$value,cutsNumber = 30)
#> [1] 0.8319696
# apply the Kolmogorov-Smirnov two-sample test for two different samples
# with the multi-statistic and antithetic approach
EpistemicTest(list1$value,list2$value,algorithm = "ms",bootstrapMethod = "anti")
#> [1] 0.8319696
# apply the Kolmogorov-Smirnov one-sample test
# with the averaging statistic approach for the first sample
AverageStatisticEpistemicTest(list1$value,sample2=NULL,cutsNumber = 30,y="pnorm")
#> [1] 0.6101717