Entropy-Based Parameter Estimation for the Four-Parameter Exponential Gamma Distribution

Song, Songbai; Song, Xiaoyan; Kang, Yan

doi:10.3390/e19050189

Cited by 11 publications

(4 citation statements)

References 25 publications

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“…The future avenues of research in this matter are: (i) to include the possibility to handle errors in the data into the MEP and the MREP principles to reconstruct the PDF of the parameters in the line started recently by Gomes-Gonçalves, Gzyl and Mayoral [39]; (ii) to extend the examples of updating using the MREP to cases in which the previous PDF is the gamma distribution or even more complex ones as the four parameters exponential gamma distribution [40]; (iii) to extend the analysis to PDF not considered in this paper as the double exponential distribution, the Fisher distribution and the logistic distribution; (iv) to generalize the updating methodology including moments and data following the ideas of Adom Giffin [41]; (v) to study more deeply Option 2 to assign PDF to operational parameters controlled by TS. that in any sample S N of size N of the variable X, exactly n elements of this sample belong to the interval [L, U] is given by the probability that the random variable Y would be equal to n. The random variable Y represent the number of sample data from S N that belongs to the interval [L, U] and follows, obviously, a binomial distribution, given by…”

Section: Discussionmentioning

confidence: 99%

Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications

Muñoz-Cobo

Mendizábal

Miquel

et al. 2017

Entropy

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Abstract:The determination of the probability distribution function (PDF) of uncertain input and model parameters in engineering application codes is an issue of importance for uncertainty quantification methods. One of the approaches that can be used for the PDF determination of input and model parameters is the application of methods based on the maximum entropy principle (MEP) and the maximum relative entropy (MREP). These methods determine the PDF that maximizes the information entropy when only partial information about the parameter distribution is known, such as some moments of the distribution and its support. In addition, this paper shows the application of the MREP to update the PDF when the parameter must fulfill some technical specifications (TS) imposed by the regulations. Three computer programs have been developed: GEDIPA, which provides the parameter PDF using empirical distribution function (EDF) methods; UNTHERCO, which performs the Monte Carlo sampling on the parameter distribution; and DCP, which updates the PDF considering the TS and the MREP. Finally, the paper displays several applications and examples for the determination of the PDF applying the MEP and the MREP, and the influence of several factors on the PDF.

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Section: Discussionmentioning

confidence: 99%

Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications

Muñoz-Cobo

Mendizábal

Miquel

et al. 2017

Entropy

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“…This can be achieved by, specifying the suitable constraints, deriving the entropy function of the Kum ( α , β ) distribution, and finally, concluding the relationship between the Lagrange multipliers and these constraints. A complete mathematical discussion of this method can be found in [ 13 ], Levine and [ 14 ], Sigh and [ 15 , 26 , 27 ].…”

Section: Methods Of Estimationmentioning

confidence: 99%

The principle of maximum entropy and the probability-weighted moments for estimating the parameters of the Kumaraswamy distribution

Helu

2022

PLoS ONE

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Since Shannon’s formulation of the entropy theory in 1940 and Jaynes’ discovery of the principle of maximum entropy (POME) in 1950, entropy applications have proliferated across a wide range of different research areas including hydrological and environmental sciences. In addition to POME, the method of probability-weighted moments (PWM), was introduced and recommended as an alternative to classical moments. The PWM is thought to be less impacted by sampling variability and be more efficient at obtaining robust parameter estimates. To enhance the PWM, self-determined probability-weighted moments was introduced by (Haktanir 1997). In this article, we estimate the parameters of Kumaraswamy distribution using the previously mentioned methods. These methods are compared to two older methods, the maximum likelihood and the conventional method of moments techniques using Monte Carlo simulations. A numerical example based on real data is presented to illustrate the implementation of the proposed procedures.

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“…The Pearson III distribution belongs to the Gamma distribution family, being a generalized form of the two-parameter Gamma distribution [10], with shifted x, and a particular case of the four-parameter gamma distribution [5,11].…”

Section: Pearson III Distribution (Pe3)mentioning

confidence: 99%

Parameter Estimation for Some Probability Distributions Used in Hydrology

Ilinca¹,

Anghel²

2022

Preprint

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Estimating the parameters of statistical distributions generally involves solving a system of nonlinear equations or a nonlinear equation, being a technical difficulty in their usual application in hydrology. This article presents improved approximations and, in some cases, new approximations for the estimation with the method of ordinary moments and the method of linear moments, which are useful for the direct calculation of the parameters, because the errors in the approximate estimation are similar to the use of iterative numerical methods. Thirteen statistical distributions of two and three parameters frequently used in hydrology are presented, for which parameter estimation was laborious. Thus, the approximate estimation of the parameters by the two methods is simple but also precise and easily applicable by hydrology researchers. The approximate forms characterized by very small errors are the result of the research conducted within the Faculty of Hydrotechnics to update the romanian normative standards in the hydrotechnical field.

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Entropy-Based Parameter Estimation for the Four-Parameter Exponential Gamma Distribution

Cited by 11 publications

References 25 publications

Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications

Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications

The principle of maximum entropy and the probability-weighted moments for estimating the parameters of the Kumaraswamy distribution

Parameter Estimation for Some Probability Distributions Used in Hydrology

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