A strategy for modelling heavy-tailed greenhouse gases (GHG) data using the generalised extreme value distribution: Are we overestimating GHG flux using the sample mean?

Dhanoa, M. S.; Louro, Aránzazu; Cardenas, L. M.; Shepherd, Anita; Sanderson, Ruth; López, Secundino

doi:10.1016/j.atmosenv.2020.117500

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…The COV is defined by Equation ().

COV = \sqrt{italicVarX} / EX

where

EX

, VarX , and

COV

are the mean value, deviation and COV of the variable

X

. Expressions of the

EX

and the VarX of Lognormal distribution, GEV distribution and Burr distribution have been given in references 31–33 . Hence, the expression of the COV of each distribution could be derived, shown in Equations (9–11):

Lognormal : {COV}_{normalL} = \sqrt{\exp (σ^{2}) - 1}

GEV : {COV}_{normalG} = \frac{|\frac{α_{normalG}}{k}| {([], normalΓ ((), 1 goodbreak+ 2 k) goodbreak- Γ^{2} ((), 1 goodbreak+ k))}^{1 / 2}}{\frac{α_{G}}{k} [1 - Γ (1 + k)] + ξ}

Burr : {COV}_{normalB} = \sqrt{\frac{B (α_{normalB} - \frac{2}{τ}, \frac{2}{τ} + 1)}{α_{normalB} B^{2} (α_{normalB} - \frac{1}{τ}, \frac{1}{τ} + 1)} - 1}

where

B (x)

is the beta function and

…”

Section: Methodsmentioning

confidence: 99%

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Analysis of sample size for friction test of short fiber reinforced polymer composites

Guan

Zhang

et al. 2023

Polymer Composites

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According to the recommendations of literature and standards, the minimum sample size for the friction test of thermoplastics is usually 3–5. While this size is valid for the friction test of neat polymer resins with homogeneous structures, its applicability to short fiber reinforced polymer composites with inhomogeneous structures remains unclear because the uneven distribution of discontinuous fibers or fillers in the matrix leads to the performance of the composites being dispersed. In this work, as a typical example, 100 friction samples made of short carbon fiber reinforced polyetherimide (SCF/PEI) composite with a typical content of 10 vol% SCFs are prepared, and their friction coefficients are measured. The maximum likelihood estimation and goodness of fit methods are employed to assess the fitting degree between the overall friction coefficient results and five mathematical distributions. The results show that the overall friction coefficient data distribution is in good agreement with the Lognormal, Generalized extreme value (GEV), and Burr distributions, respectively. Based on the fitting result, the minimum sample size is analyzed by Monte Carlo Simulation. It shows that the minimum sample size strongly depends on the property dispersion parameter (COV: coefficient of variation). Based on this parameter, the minimum sample size is given. In a practical test, the performance dispersion degree of a composite cannot be known in advance, hence a sample size determination method is proposed to yield a reasonable performance description parameter by applying the results of this work, and this method is validated by the overall test data.Highlights Proposed a sample size determination method for practical friction tests. The minimum sample size for the friction test is yielded statistically. The minimum sample size strongly depends on a property dispersion parameter.

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“…The COV is defined by Equation ().

COV = \sqrt{italicVarX} / EX

where

EX

, VarX , and

COV

are the mean value, deviation and COV of the variable

X

. Expressions of the

EX

Lognormal : {COV}_{normalL} = \sqrt{\exp (σ^{2}) - 1}

GEV : {COV}_{normalG} = \frac{|\frac{α_{normalG}}{k}| {([], normalΓ ((), 1 goodbreak+ 2 k) goodbreak- Γ^{2} ((), 1 goodbreak+ k))}^{1 / 2}}{\frac{α_{G}}{k} [1 - Γ (1 + k)] + ξ}

Burr : {COV}_{normalB} = \sqrt{\frac{B (α_{normalB} - \frac{2}{τ}, \frac{2}{τ} + 1)}{α_{normalB} B^{2} (α_{normalB} - \frac{1}{τ}, \frac{1}{τ} + 1)} - 1}

where

B (x)

is the beta function and

…”

Section: Methodsmentioning

confidence: 99%

“…Expressions of the EX and the VarX of Lognormal distribution, GEV distribution and Burr distribution have been given in references. [31][32][33] Hence, the expression of the COV of each distribution could be derived, shown in Equations (9)(10)(11):…”

Section: Sample Size Analysismentioning

confidence: 99%

Analysis of sample size for friction test of short fiber reinforced polymer composites

Guan

Zhang

et al. 2023

Polymer Composites

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show abstract

“…The major limitation of using Box-Cox transformation is its poor performance in handling long-tailed or skew data (Zhu and Melnykov 2018;Dhanoa et al 2020). Another limitation of Box-Cox transformation is its incompatibility with a normal error distribution (Eriksson et al 2019).…”

Section: Transformations Applied To Achieve Normalitymentioning

confidence: 99%

Transformational Approach to Analytical Value-at-Risk for near Normal Distributions

Prakash

Sangwan

Singh

2021

JRFM

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In this paper, we extend the parametric approach of VaR estimation that is based upon the application of two transforms, one for handling skewness and other for kurtosis. These transformations restore normality to data when applied in succession. The transforms are well defined and offer an alternative to VaR models based on the variance–covariance approach. We demonstrate the application of the technique using three pairs of uncorrelated but negatively skewed and fat-tailed stock return distributions, one pair each from recent periods in US and international market, and one from the stressed period of US economic history. Furthermore, we extend the analysis to economic domain by calculating expected shortfalls and risk capital under different estimation methods. For the sake of completion, we compare the estimation results of normal and transformation methods to non-parametric historical simulation.

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An analysis of Earth temperature and related series in air and soil

Dhanoa¹,

Sanderson²,

Shepherd³

et al. 2023

Advances in Agronomy

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A strategy for modelling heavy-tailed greenhouse gases (GHG) data using the generalised extreme value distribution: Are we overestimating GHG flux using the sample mean?

Cited by 6 publications

References 21 publications

Analysis of sample size for friction test of short fiber reinforced polymer composites

Analysis of sample size for friction test of short fiber reinforced polymer composites

Transformational Approach to Analytical Value-at-Risk for near Normal Distributions

An analysis of Earth temperature and related series in air and soil

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