Using Imperfectly Elicited Fractiles for the Estimation of Probability Distribution Parameters

2012 ◽  
Author(s):  
Saurabh Bansal ◽  
Genaro Gutierrez
Keyword(s):  
Probability Distribution ◽  
Distribution Parameters

scholarly journals Ranking the scientific output of researchers in fractional calculus

2019 ◽  
Vol 22 (1) ◽  
pp. 11-26 ◽  
Author(s):  
J. A. Tenreiro Machado ◽  
António M. Lopes
Keyword(s):  
Probability Distribution ◽  
Fractional Calculus ◽  
Multidimensional Scaling ◽  
Gamma Distribution ◽  
Scientific Output ◽  
Second Phase ◽  
Scaling Technique ◽  
3 Dimensional ◽  
Distribution Parameters ◽  
Canberra Distance

Abstract This paper analyses the citation profiles (CP) of 130 researchers in fractional calculus. In a first phase, the Canberra distance is used to measure the similarities between the researchers’ CP, and the multidimensional scaling technique (MDS) is adopted for processing and visualizing the information. In a second phase, the gamma probability distribution is used to fit the normalized CP and the gamma parameters are used to characterize the researchers. The MDS results and the gamma distribution parameters are represented graphically in 2- and 3-dimensional locus depicting the relative positions of the researchers.

Evaluation of simple quantile estimation functions for modeling forest diameter distributions in even-aged stands of interior Douglas-fir

1993 ◽  
Vol 23 (11) ◽  
pp. 2376-2382 ◽  
Author(s):  
James D. Newberry ◽  
James A. Moore ◽  
Lianjun Zhang
Keyword(s):  
Probability Distribution ◽  
Order Statistics ◽  
Estimation Method ◽  
Douglas Fir ◽  
Quantile Estimation ◽  
Distribution Free ◽  
Inland Northwest ◽  
Distribution Parameters ◽  
Solving Equations ◽  
Diameter Distributions

The method of percentiles usually involves simultaneously solving equations for probability distribution parameters as functions of sample-based estimates of the appropriate quantiles. Eight simple distribution-free methods for estimating quantiles from sample-based order statistics were evaluated empirically using even-aged Douglas-fir (Pseudotsugamenziesii var. glauca (Beissn.) Franco) diameter distributions from the Inland Northwest. Two methods, calculated by weighting adjacent order statistics, consistently gave the best results for both the Weibull and Johnson's SB distributions. Certain distributional shapes were also evaluated to determine if they influenced the quantile estimation method. Although some influence was detected, the best methods were usually best across all categories.

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.

scholarly journals Spectral Probability Distribution of Closed Connected Water and Remote Sensing Statistical Inference for Yellow Substance

2021 ◽  
Vol 87 (11) ◽  
pp. 807-819
Author(s):  
Weining Zhu ◽  
Zeliang Zhang ◽  
Zaiqiao Yang ◽  
Shuna Pang ◽  
Jiang Chen ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Probability Distribution ◽  
Statistical Inference ◽  
Probability Distributions ◽  
Landsat 8 ◽  
Inference Models ◽  
Yellow Substance ◽  
Water Classification ◽  
Distribution Scheme ◽  
Distribution Parameters

Unlike traditional remote sensing inversion, this study proposes a new distribution–distribution scheme, which uses statistical inferences to estimate the probability distribution of in-water components based on the probability distribution of the observed spectra. The distribution–distribution scheme has the advantages that it rapidly gives the statistical information of the water of interest, assists the traditional scheme in improving models, and provides more valuable information for water classification and aquatic environment analysis. In this study, based on Landsat-8 images, we analyzed the spectral probability distributions of 688 global waters and found that many of them were normal, log normal, and exponential distributions with diverse patterns in distribution parameters such as the mean, standard deviation, skewness, and kurtosis. Using simulated and field-measured data, we propose a bootstrap-based distribution–distribution scheme and develop some simple remote sensing statistical inference models to estimate the distribution parameters of yellow substance in water.

scholarly journals Improving the Robustness of Entangled States by Basis Transformation

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 59 ◽  
Author(s):  
Xin-Wen Wang ◽  
Shi-Qing Tang ◽  
Yan Liu ◽  
Ji-Bing Yuan
Keyword(s):  
Probability Distribution ◽  
Quantum Entanglement ◽  
Error Distribution ◽  
Entangled States ◽  
Noise Strength ◽  
Practical Application ◽  
Distribution Parameters ◽  
The Right ◽  
Qubit States ◽  
Computational Basis

In the practical application of quantum entanglement, entangled particles usually need to be distributed to many distant parties or stored in different quantum memories. In these processes, entangled particles unavoidably interact with their surrounding environments, respectively. We here systematically investigate the entanglement-decay laws of cat-like states under independent Pauli noises with unbalanced probability distribution of three kinds of errors. We show that the robustness of cat-like entangled states is not only related to the overall noise strength and error distribution parameters, but also to the basis of qubits. Moreover, we find that whether a multi-qubit state is more robust in the computational basis or transversal basis depends on the initial entanglement and number of qubits of the state as well as the overall noise strength and error distribution parameters of the environment. However, which qubit basis is conductive to enhancing the robustness of two-qubit states is only dependent on the error distribution parameters. These results imply that one could improve the intrinsic robustness of entangled states by simply transforming the qubit basis at the right moment. This robustness-improving method does not introduce extra particles and works in a deterministic manner.

scholarly journals Probability Distribution of Cross-sectional radius of Corroded Steel Bars in Concrete and Its application

2018 ◽  
Vol 199 ◽  
pp. 04008
Author(s):  
LI Chongkai ◽  
ZHANG Weiping ◽  
GU Xianglin ◽  
HUANG Qinghua
Keyword(s):  
Probability Distribution ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Gumbel Distribution ◽  
Current Method ◽  
Distribution Model ◽  
Cross Sectional ◽  
Steel Bars ◽  
Distribution Parameters ◽  
The Cross

The impress current method is applied to acquire corroded steel bars embedded in concrete, and three-dimensional(3D) laser scanning techniques are applied on corroded steel bars to obtain the cross-sectional radius of corroded steel bars. Statistical analysis shows that with the increase of corrosion degree, the variation of radius of corroded steel bars increases linearly. For different types of steel bars, plain round steel bars have a larger sensitivity to corrosion than ribbed ones. Original radius of steel bars and mixture proportion of concrete have negligible effect on the variability of radius of corroded steel bars. A normal distribution model is obtained to describe radius data of corroded steel bars. For the convenience of practical application, the indicator, R, which is the ratio of the average to the minimum cross-sectional areas of corroded steel bars, is introduced to quantify the longitudinal variation of the cross-sectional areas. By using Monte-Carlo simulation, the indicator, R, of corroded steel bars are achieved based on the probability distribution of radius. The indicator R can be fitted well by the Gumbel distribution, and the distribution parameters increase linearly with the increases of corrosion degree.

scholarly journals MÉTODOS ESTIMADORES DOS PARÂMETROS DA DISTRIBUIÇÃO DE GUMBEL E SUA INFLUÊNCIA EM ESTUDOS HIDROLÓGICOS DE PROJETO

Irriga ◽  
2005 ◽  
Vol 10 (4) ◽  
pp. 334-350 ◽  
Author(s):  
Carlos Rogério de Mello ◽  
Antônio Marciano da Silva
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Daily Rainfall ◽  
Rio Grande ◽  
Likelihood Method ◽  
Estimated Parameters ◽  
Historical Series ◽  
Distribution Parameters ◽  
Rainfall Runoff Model ◽  
Runoff Model

MÉTODOS ESTIMADORES DOS PARÂMETROS DA DISTRIBUIÇÃO DE GUMBEL E SUA INFLUÊNCIA EM ESTUDOS HIDROLÓGICOS DE PROJETO  Carlos Rogério de Mello; Antônio Marciano da SilvaLaboratório de Hidráulica, Departamento de Engenharia, Universidade Federal de Lavras, Lavras, MG, [email protected]  1 RESUMO             Este trabalho objetiva estudar os efeitos que o método de estimativa dos parâmetros da distribuição de Gumbel proporcionam na estimativa da equação de chuvas intensas aplicando-se um modelo chuva-vazão, a conseqüente influência no hidrograma de projeto. Trabalhou-se com 7 estações pluviométricas da região Alto Rio Grande, ajustando-se a distribuição Gumbel à série histórica de precipitação máxima diária anual, pelas metodologias da Máxima Verossimilhança e Momentos. Utilizando o método de desagregação de chuvas, estimaram-se as respectivas equações de chuvas intensas. Com o método CN-SCS foram gerados os hidrogramas de projeto para uma bacia hidrográfica hipotética. Por meio do teste de l2, foram feitas comparações entre os modelos ajustados pelas metodologias. Verificou-se que as séries históricas ajustadas por Máxima Verossimilhança produziram os menores valores de l2, concluindo sobre a sua maior precisão. No entanto, os efeitos na geração da equação de chuvas intensas e por conseqüência, no hidrograma de projeto, apresentaram variações que, em alguns casos, foram de magnitude considerável, e em outros, de menor relevância em termos práticos. UNITERMOS: equação de chuvas intensas, máxima verossimilhança, método dos momentos.  MELLO, C.R.de; SILVA, A. M. da. ESTIMATING METHODS OF GUMBEL PROBABILITY DISTRIBUTION PARAMETERS AND THEIR INFLUENCE ON DESIGN HYDROLOGIC STUDIES  2 ABSTRACT             This work aimed to evaluate the influence of parameter estimating methods of Gumbel probability distribution for adjustment of p-d-f rainfall equation and, through rainfall-runoff model, generation of design hydrograph. Maximum annual daily rainfall from seven (7) weather stations, belonging to Alto Rio Grande region, were used and Gumbel probability distribution was adjusted to its parameters, which were estimated by the methods of Maximum Likelihood and Moment. Qui-square statistical test was applied to evaluate the accuracy of both methods. Desegregation rainfall technique was applied to estimate the respective p-d-f rainfall equations. CN-SCS method was used, based on estimated p-d-f rainfall equations to generate the design hydrograph for a hypothetical watershed. Through qui-squared test, adjusted methods were compared using different methodologies. Historical series that were adjusted by estimated parameters of Maximum Likelihood were more accurate, based on slower qui-square. However, effects on p-d-f rainfall equations and design hydrograph showed considerable differences in any situations, but in others these variations had smaller relevance in practical situations. KEYWORDS: p-d-f rainfall equation, Maximum Likelihood, Method of Moments.

Application of SAP2000 API and .NET Framework for Reliability Assessment of RC Structures

2014 ◽  
Vol 578-579 ◽  
pp. 1482-1488
Author(s):  
Qing Jun Chen ◽  
Da Xin Liu ◽  
Inamullah Khan ◽  
Jian Cai ◽  
Fan Bai
Keyword(s):  
Probability Distribution ◽  
Structure Analysis ◽  
Engineering Application ◽  
Rc Structures ◽  
Reliability Indices ◽  
Reliability Indicators ◽  
Distribution Parameters ◽  
Practical Program ◽  
Integral Structure ◽  
Net Framework

Based on the results of integral structure analysis, a practical program for the reliability analysis of the members is introduced for engineering application. The .NET framework and SAP2000 API were combined to develop this program. The probability distribution parameters of the load and the material are the input parameters and then based on the integral structure analysis results, by combining the Monte Carlo simulation methods and the JC methods, the probability distribution of the load effects and the resistance of the members can be calculated, thus the reliability indices of each member could be obtained. Furthermore, an example was introduced and the comparative study between this proposed method and the conventional method for evaluation of a structure was carried out. The results show that it is a feasible method to evaluate the bearing capacity of a structure by exploiting reliability indices directly and this method can offer more quantitative reliability indicators of the structures.

Sign in / Sign up

Export Citation Format

Share Document