scholarly journals A Model of Fuzzy Normal Distribution

2016 ◽  
Vol 06 (05) ◽  
pp. 749-755
Author(s):  
Haoge Liu ◽  
Jianhe Guan
Keyword(s):  
Normal Distribution ◽  
Fuzzy Normal Distribution

Credibility Hypothesis Testing of Variance of Fuzzy Normal Distribution

2017 ◽  
pp. 193-220
Author(s):  
S. Sampath ◽  
B. Ramya
Keyword(s):  
Hypothesis Testing ◽  
Normal Distribution ◽  
Test Procedures ◽  
Rejection Region ◽  
Ratio Criterion ◽  
Expected Values ◽  
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.

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

2020 ◽  
Vol 8 (5) ◽  
pp. 183-198
Author(s):  
Marcus Pinto da Costa da Rocha ◽  
Lucelia M. Lima ◽  
Valcir J. C. Farias ◽  
Benjamin Bedregal ◽  
Heliton R. Tavares
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Portfolio Selection ◽  
Real Data ◽  
Laplace Distribution ◽  
Fuzzy Probability ◽  
Variance Model ◽  
Risk Rate ◽  
Mean Variance ◽  
Fuzzy Normal Distribution

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.

On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

Interrelations of Thrombo-Embolic Diseases and Blood-Group Distribution

1963 ◽  
Vol 09 (02) ◽  
pp. 472-474 ◽  
Author(s):  
W Dick ◽  
W Schneider ◽  
K Brockmüller ◽  
W Mayer
Keyword(s):  
Normal Distribution ◽  
Blood Group ◽  
Blood Groups ◽  
The Other ◽  
Other Hand ◽  
Group Distribution

SummaryA comparison between the repartition of the blood groups in 461 patients suffering from thromboembolic disorders and the normal distribution has shown a statistically ascertained predominance of the group A1. On the other hand the blood groups 0 and A2 are distinctly less frequent than in the normal distribution.

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