A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection

The propose of this work is applied the fuzzy Laplace distribution on a possibilistic mean-variance model presented by Li et al which appliehe fuzzy normal distribution. The theorem necessary to introduce the Laplace distribution in the model was demonstrated. It was made an analysis of the behavior of the fuzzy normal and fuzzy Laplace distributions on the portfolio selection with VaR constraint and risk-free investment considering real data. The results showns that were not difference in assets selection and in return rate, however, There was a change in the risk rate, which was higher in the Laplace distribution than in the normal distribution.

Credibility Hypothesis Testing of Variance of Fuzzy Normal Distribution

This paper considers the problem of developing test procedures for testing credibility hypotheses about the variance of fuzzy normal distribution assuming the expected values of the distributions mentioned under null and alternative credibility hypotheses are known and equal. The cases where the underlying hypothesis is simple and composite (one sided) are considered. Tests have been derived with the help of the membership ratio criterion. Properties possessed by the developed tests, like best credibility rejection region and uniformly best rejection region have been studied. Examples are also given to illustrate the usage of the derived tests.