On the formalization of fuzzy random variables
Information Sciences: an International Journal - Fuzzy random variables
Two-sample hypothesis tests of means of a fuzzy random variable
Information Sciences: an International Journal - Fuzzy random variables
Tools for fuzzy random variables: Embeddings and measurabilities
Computational Statistics & Data Analysis
Bootstrap approach to the multi-sample test of means with imprecise data
Computational Statistics & Data Analysis
Triangular fuzzification of random variables and power of distribution tests: Empirical discussion
Computational Statistics & Data Analysis
Fuzzy Sets and Systems
Favorability functions based on kernel density estimation for logistic models: A case study
Computational Statistics & Data Analysis
The fuzzy approach to statistical analysis
Computational Statistics & Data Analysis
Tools for fuzzy random variables: Embeddings and measurabilities
Computational Statistics & Data Analysis
Bootstrap approach to the multi-sample test of means with imprecise data
Computational Statistics & Data Analysis
Centrality as a gradual notion: A new bridge between fuzzy sets and statistics
International Journal of Approximate Reasoning
Fuzzy data treated as functional data: A one-way ANOVA test approach
Computational Statistics & Data Analysis
The median of a random fuzzy number. The 1-norm distance approach
Fuzzy Sets and Systems
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A family of fuzzy representations of random variables is presented. Each representation transforms a real-valued random variable into a fuzzy-valued one. These representations can be chosen so that they lead to fuzzy random variables whose means capture different relevant information on the probability distribution of the original real-valued random variable. In this way, the means of the transformed fuzzy random variables can capture, for instance, immediate visual information about some key parameters, and even the whole information about the distribution of the original random variable. Representations capturing visual information on parameters of the original random variable may be considered for statistical descriptive/exploratory purposes. Representations for which the fuzzy mean characterizes the distribution of the original random variable will be mainly valuable to develop statistical inferences on this variable. Some interesting inferential applications for classical random variables based on the last fuzzy representations are commented, and an example illustrates one of them empirically and motivate future directions and discussions.