Expansion of Perturbed Random Variables Based on Generalized Wiener Functionals

On Convergence rate of Wiener-Ito expansion for generalized random variables

In the past few years, there has been growing interest in numerical methods for stochastic partial differential equations (SPDEs): see [1–3,5,6,8–11,13,14]. One of the important topics is the numerical approximation of solutions to SPDEs, where some of the coefficients are random variables. Some of the interesting approaches are spectral finite element methods using formal Hermite polynomial ch...

Generalized Wiener filtering for positive alpha-stable random variables Filtrage de Wiener généralisé pour des variables aléatoires positives alpha-stables

This report provides a mathematical proof of a result which is a generalization of Wiener filtering to Positive α-stable (PαS) distributions, a particular subclass of the α-stable distributions family whose support is [0;+∞[. PαS distributions are useful to model nonnegative data and since they are heavy-tailed, they present a natural robustness to outliers. In applications such as nonnegative ...

OPTIMAL STATISTICAL TESTS BASED ON FUZZY RANDOM VARIABLES

A novel approach is proposed for the problem of testing statistical hypotheses about the fuzzy mean of a fuzzy random variable.The concept of the (uniformly) most powerful test is extended to the (uniformly) most powerful fuzzy-valued test in which the test function is a fuzzy set representing the degrees of rejection and acceptance of the hypothesis of interest.For this purpose, the concepts o...

Local Functionals and Generalized Random Fields

ESTIMATORS BASED ON FUZZY RANDOM VARIABLES AND THEIR MATHEMATICAL PROPERTIES

In statistical inference, the point estimation problem is very crucial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum ...