Level-Wise Statistics for Fuzzy Random Variables

Level-wise statistical methods for fuzzy random variables, implementing the Puri-Ralescu framework. Provides level-wise empirical distribution functions, moments, covariance and correlation, a level-wise Kolmogorov-Smirnov goodness-of-fit test, an approximate fuzzy normal distribution with simulation, and level-wise central limit theorem and law of large numbers inference. The package only depends on base R.

FuzzyRandom

Level-wise (Puri--Ralescu) statistics for fuzzy random variables.

Fuzzy numbers are represented through their alpha-level cuts [X^-(alpha), X^+(alpha)], and every statistical operator acts level-wise so that the expectation, variance, covariance, empirical distribution, goodness-of-fit, central limit theorem and law of large numbers all live in a single coherent framework.

Installation

Install from source (after R CMD build / R CMD INSTALL):

# install.packages("remotes")
remotes::install_dir("path/to/FuzzyRandom")

Quick start

library(FuzzyRandom)
set.seed(123)
s <- rnorm_fuzzy(80, triangular_fuzzy(0, 1, 2), diag(2) * 0.25)

plot(s)
plot(fuzzy_ecdf(s))
ks_test(s, p0 = "pnorm")

cl <- clt(s)
summary(cl)
plot(s <- simulate(cl, nsim = 60))