A goodness-of-fit test based on Bézier curve estimation of Kendall distribution

Susam, Selim Orhun; Ucer, Burcu Hudaverdi

doi:10.1080/00949655.2020.1720680

Cited by 14 publications

(8 citation statements)

References 34 publications

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“…The datasheet specifications of these four commercial PEMFCs stacks are concluded from [14,25,49,50], and represented in Table 1, respectively. The measured experimental data characteristic curves of these four FCs are accessible online and reproducible in the literature in terms of parameter and curves estimation by several researchers [14,19,38,46]. The efficiency of the proposed effective computer graphic technique used to approximate the FC characteristics curve is compared with various algorithms to validate the performance of each algorithm.…”

Section: Results Discussion and Comparisonsmentioning

confidence: 99%

“…The last case study deals with the approximation of the characteristics curve of the 250 W fuel cell stack. The measured end experimental current and voltage data are collected from [46]. This data is widely used in the parameters extraction and estimation to estimate the characteristic curve of the 250 W fuel cell stack.…”

Section: Case Study 4: 250 W Pemfc Stackmentioning

confidence: 99%

“…For example, Huo et al [44] have applied the Bézier curve technique to approach and design the trajectory of the electric sail. A description of the thermal behavior of three-way mixing valves [45], estimation of the Kendall distribution function [46], and circle, and conic approximation [47,48], has been also carried out.…”

Section: Introductionmentioning

confidence: 99%

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Fuel Cell Characteristic Curve Approximation Using the Bézier Curve Technique

2020

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Accurate modelling of the fuel cell characteristics curve is essential for the simulation analysis, control management, performance evaluation, and fault detection of fuel cell power systems. However, the big challenge in fuel cell modelling is the multi-variable complexity of the characteristic curves. In this paper, we propose the implementation of a computer graphic technique called Bézier curve to approximate the characteristics curves of the fuel cell. Four different case studies are examined as follows: Ballard Systems, Horizon H-12 W stack, NedStackPS6, and 250 W proton exchange membrane fuel cells (PEMFC). The main objective is to minimize the absolute errors between experimental and calculated data by using the control points of the Bernstein–Bézier function and de Casteljau’s algorithm. The application of this technique entails subdividing the fuel cell curve to some segments, where each segment is approximated by a Bézier curve so that the approximation error is minimized. Further, the performance and accuracy of the proposed techniques are compared with recent results obtained by different metaheuristic algorithms and analytical methods. The comparison is carried out in terms of various statistical error indicators, such as Individual Absolute Error (IAE), Relative Error (RE), Root Mean Square Error (RMSE), Mean Bias Errors (MBE), and Autocorrelation Function (ACF). The results obtained by the Bézier curve technique show an excellent agreement with experimental data and are more accurate than those obtained by other comparative techniques.

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Section: Results Discussion and Comparisonsmentioning

confidence: 99%

Section: Case Study 4: 250 W Pemfc Stackmentioning

confidence: 99%

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Fuel Cell Characteristic Curve Approximation Using the Bézier Curve Technique

2020

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“…In contrast, the empirical beta copula is a special case of the empirical Bernstein copula, which relies on Bernstein polynomials; see Sancetta and Satchell (2004). When nonparametrically estimating a bivariate AC using Bernstein polynomials, the Kendall distribution function can be estimated using B‐splines or Bezier curve; as in Susam and Ucer (2020). Lin et al (2017) proposed a procedure for nonparametric estimation of multivariate conditional copulae using local linear smoothing in the kernel estimation and then using the Newton–Raphson method to minimize the estimated likelihood.…”

Section: Estimation Methods For Copulaementioning

confidence: 99%

“…Moreover, the approach using Kendall's distribution can also be used together with Bernstein polynomials and Bezier curves. Here we have the advantage that the power of the test can be adapted by choosing the degree of the Bernstein polynomial or Bezier curves, as shown in Susam and Ucer (2018) and (2020).…”

Section: Dependence Measures and Goodness‐of‐fit Tests For Copulaementioning

confidence: 99%

Copulae: An overview and recent developments

Größer

Okhrin

2021

WIREs Computational Stats

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Over the decades that have passed since they were introduced, copulae still remain a very powerful tool for modeling and estimating multivariate distributions. This work gives an overview of copula theory and it also summarizes the latest results. This article recalls the basic definition, the most important cases of bivariate copulae, and it then proceeds to a sketch of how multivariate copulae are developed both from bivariate copulae and from scratch. Regarding higher dimensions, the focus is on hierarchical Archimedean, vine, and factor copulae, which are the most often used and most flexible ways to introduce copulae to multivariate distributions. We also provide an overview of how copulae can be used in various fields of data science, including recent results. These fields include but are not limited to time series and machine learning. Finally, we describe estimation and testing methods for copulae in general, their application to the presented copula structures, and we give some specific testing and estimation procedures for those specific copulae.

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