FOUR MODELS TO CALCULATE A FUZZY PROBABILITY DISTRIBUTION WITH A SMALL SAMPLE

2007 ◽  
Vol 06 (04) ◽  
pp. 611-623 ◽  
Author(s):  
CHONGFU HUANG ◽  
TIAN ZONG ◽  
ZHIFEN CHEN
Keyword(s):  
Probability Distribution ◽  
Natural Disaster ◽  
Small Sample ◽  
Fuzzy Probability ◽  
System Calls ◽  
Fuzzy Methods ◽  
Disaster System

The need to cope with complicated natural disaster system calls for a sophisticated way of analyzing it with the help of fuzzy methods. Therefore, four models are suggested succeedingly to represent a fuzzy probability distribution with a small sample. In this paper, we inspect the four models in detail and evaluate their performance on an emulation test.

Zygosity Partitioning of Small Twin Samples

1985 ◽  
Vol 34 (3-4) ◽  
pp. 167-174 ◽  
Author(s):  
Gordon Allen ◽  
Zdenek Hrubec
Keyword(s):  
Probability Distribution ◽  
Small Sample ◽  
Source Population

AbstractWhen the Weinberg estimate of the proportion of monozygotic pairs is quite deviant from that in the source population, it is likely to be wrong because Weinberg's difference is much less stable than the zygosity proportions. A formula is proposed for the probability distribution of possible compositions of a small sample of twins based on sex concordance in the sample and zygosity proportions in the source population.

A Method of Fuzzy Probability under Small Sample

2008 ◽  
Vol 44-46 ◽  
pp. 879-884 ◽  
Author(s):  
Hai An ◽  
Wei Guang An ◽  
Y.L. Zhao ◽  
Zheng Ji Song
Keyword(s):  
Membership Function ◽  
Prior Information ◽  
Population Distribution ◽  
Normal Population ◽  
Small Sample ◽  
Fuzzy Membership Function ◽  
Fuzzy Probability ◽  
Processing Theory ◽  
Fuzzy Parameter ◽  
The Membership Function

Based on BAYES data processing theory, a new method of fuzzy probability is proposed for the parameter reliability of small sample. Prior distribution of fuzzy parameter is obtained by stochastic weighted method, then posterior distribution of fuzzy parameter is got by the method of conjugate distribution. In the end, the formula of fuzzy membership function is constructed, and probability of fuzzy events is solved.The study of this paper aims at the membership function which is deduced in the condition that mean is known and deviation is unknown in normal population distribution. At the same time using information of small sample of actual experiment, the study fully utilizes prior information, so, it is convincing to evaluate reliability of fuzzy parameter. It is obviously economical.

scholarly journals Fuzzy reliability analysis based on support vector machine

2021 ◽  
Author(s):  
xiao bo Nie ◽  
Haibin Li ◽  
Hongxia Chen ◽  
Ruying Pang ◽  
Honghua Sun
Keyword(s):  
Support Vector Machine ◽  
Probability Distribution ◽  
Reliability Analysis ◽  
Small Sample ◽  
Learning Ability ◽  
Support Vector ◽  
Fuzzy Reliability ◽  
Performance Function ◽  
Sample Data ◽  
Distribution Parameters

Abstract For a structure with implicit performance function structure and less sample data, it is difficult to obtain accurate probability distribution parameters by traditional statistical analysis methods. To address the issue, the probability distribution parameters of samples are often regarded as fuzzy numbers. In this paper, a novel fuzzy reliability analysis method based on support vector machine is proposed. Firstly, the fuzzy variable is converted into an equivalent random variable, and the equivalent mean and equivalent standard deviation are calculated. Secondly, the support vector regression machine with excellent small sample learning ability is used to train the sample data. Subsequently, and the performance function is approximated. Finally, the Monte Carlo method is used to obtain fuzzy reliability. Numerical examples are investigated to demonstrate the effectiveness of the proposed method, which provides a feasible way for fuzzy reliability analysis problems of small sample data.

Drought risk analysis of maize under climate change based on natural disaster system theory in Southwest China

2016 ◽  
Vol 36 (5) ◽  
pp. 340-349 ◽  
Author(s):  
Jian-ying Jia ◽  
Lan-ying Han ◽  
Yi-feng Liu ◽  
Nan He ◽  
Qiang Zhang ◽  
...  
Keyword(s):  
Climate Change ◽  
System Theory ◽  
Risk Analysis ◽  
Natural Disaster ◽  
Southwest China ◽  
Drought Risk ◽  
Disaster System

scholarly journals The Smoothed Bootstrap Fine-Tuning

2019 ◽  
Vol 1 (1) ◽  
pp. 716-723
Author(s):  
Renata Dwornicka ◽  
Andrii Goroshko ◽  
Jacek Pietraszek
Keyword(s):  
Probability Distribution ◽  
Empirical Distribution ◽  
Bootstrap Method ◽  
Small Sample ◽  
Fine Tuning ◽  
Smoothed Bootstrap ◽  
Full Probability ◽  
The Bootstrap Method

AbstractThe bootstrap method is a well-known method to gather a full probability distribution from the dataset of a small sample. The simple bootstrap i.e. resampling from the raw dataset often leads to a significant irregularities in a shape of resulting empirical distribution due to the discontinuity of a support. The remedy for these irregularities is the smoothed bootstrap: a small random shift of source points before each resampling. This shift is controlled by specifically selected distributions. The key issue is such parameter settings of these distributions to achieve the desired characteristics of the empirical distribution. This paper describes an example of this procedure.

scholarly journals Reliability Evaluation for the Running State of the Manufacturing System Based on Poor Information

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Xintao Xia ◽  
Wenhuan Zhu ◽  
Bin Liu
Keyword(s):  
Probability Distribution ◽  
Product Quality ◽  
Manufacturing System ◽  
Evaluation Method ◽  
Probability Distributions ◽  
Bootstrap Method ◽  
Maximum Entropy Principle ◽  
Reliability Evaluation ◽  
Small Sample ◽  
Inspection Data

The output performance of the manufacturing system has a direct impact on the mechanical product quality. For guaranteeing product quality and production cost, many firms try to research the crucial issues on reliability of the manufacturing system with small sample data, to evaluate whether the manufacturing system is capable or not. The existing reliability methods depend on a known probability distribution or vast test data. However, the population performances of complex systems become uncertain as processing time; namely, their probability distributions are unknown, if the existing methods are still taken into account; it is ineffective. This paper proposes a novel evaluation method based on poor information to settle the problems of reliability of the running state of a manufacturing system under the condition of small sample sizes with a known or unknown probability distribution. Via grey bootstrap method, maximum entropy principle, and Poisson process, the experimental investigation on reliability evaluation for the running state of the manufacturing system shows that, under the best confidence levelP=0.95, if the reliability degree of achieving running quality isr>0.65, the intersection area between the inspection data and the intrinsic data isA(T)>0.3and the variation probability of the inspection data isPB(T)≤0.7, and the running state of the manufacturing system is reliable; otherwise, it is not reliable. And the sensitivity analysis regarding the size of the samples can show that the size of the samples has no effect on the evaluation results obtained by the evaluation method. The evaluation method proposed provides the scientific decision and suggestion for judging the running state of the manufacturing system reasonably, which is efficient, profitable, and organized.

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