<b>extremefit</b>: A Package for Extreme Quantiles

Durrieu, Gilles; Grama, Ion; Jaunatre, Kevin; Pham, Quang-Khoai; Tricot, Jean-Marie

doi:10.18637/jss.v087.i12

Cited by 9 publications

(10 citation statements)

References 37 publications

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“…Let F t (x) = P (X ≤ x | T = t), where X is a random variable given at time index t ∈ [0, T max ]. The excess distribution function over a sufficiently high threshold µ is then given by [17,18]:…”

Section: Semi-parametric Extremal Mixture Modelmentioning

confidence: 99%

“…where the parameter θ > 0 denotes the conditional tail index (extremal index) and an unknown threshold µ ≥ x 0 , which depends on t. The distribution function F t can be approximated by the empirical distribution function. The semi-parametric extremal mixture model (SPEM) is defined by [17,18]:…”

Section: Semi-parametric Extremal Mixture Modelmentioning

confidence: 99%

“…Reference [21] developed a time-varying threshold which is coupled with a positive shift factor. In this present study, the selection of the threshold is done by testing a goodness-of-fit test discussed by reference [18], for the parametric part of the model 3. The k upper statistics are used to test the tail adjustment of Pareto distribution.…”

Section: Threshold Selectionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of Extreme Quantiles of Global Horizontal Irradiance: A Comparative Analysis Using an Extremal Mixture Model and a Generalised Additive Extreme Value Model

Ravele¹,

Sigauke²,

Jhamba³

2022

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Solar power poses challenges to the management of grid energy due to its intermittency. To have an optimal integration of solar power on the electricity grid it is important to have accurate forecasts. This study discusses the comparative analysis of semi-parametric extremal mixture (SPEM), generalised additive extreme value (GAEV) or quantile regression via asymmetric Laplace distribution (QR-ALD), additive quantile regression (AQR-1), additive quantile regression with temperature variable (AQR-2) and penalised cubic regression smoothing spline (benchmark) models for probabilistic forecasting of hourly global horizontal irradiance (GHI) at extremely high quantiles (τ = 0.95, 0.97, 0.99, 0.999 and 0.9999). The data used are from the University of Venda radiometric in South Africa and are from the period 1 January 2020 to 31 December 2020. Empirical results from the study showed that the AQR-2 is the best fitting model and gives the most accurate prediction of quantiles at τ = 0.95, 0.97, 0.99 and 0.999, while at 0.9999-quantile the GAEV model has the most accurate predictions. Based on these results it is recommended that the AQR-2 and GAEV models be used for predicting extremely high quantiles of hourly GHI in South Africa. The predictions from this study are valuable to power utility decision-makers and system operators when making highrisk decisions and regulatory frameworks that require high-security levels. This is the first application to conduct a comparative analysis of the proposed models using South African solar irradiance data, to the best of our knowledge.

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Section: Semi-parametric Extremal Mixture Modelmentioning

confidence: 99%

Section: Semi-parametric Extremal Mixture Modelmentioning

confidence: 99%

Section: Threshold Selectionmentioning

confidence: 99%

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Estimation of Extreme Quantiles of Global Horizontal Irradiance: A Comparative Analysis Using an Extremal Mixture Model and a Generalised Additive Extreme Value Model

Ravele¹,

Sigauke²,

Jhamba³

2022

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“…We seek to estimate extreme quantiles, i.e., F −1 t (τ) for 0.950 ≤ τ ≤ 0.9999. Now, if F t is in the domain of attraction of the Fr échet distribution, then the excess distribution function given in Equation ( 1) can be estimated by a Pareto distribution in Equation (2) [37]:…”

Section: Semi-parametric Extremal Mixture Modelsmentioning

confidence: 99%

Prediction of Extreme Conditional Quantiles of Electricity Demand: An Application Using South African Data

2021

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It is important to predict extreme electricity demand in power utilities as the uncertainties in the future of electricity demand distribution have to be taken into consideration to achieve the desired goals. The study focused on the prediction of extremely high conditional quantiles (between 0.95 and 0.9999) and extremely low quantiles (between 0.001 and 0.05) of electricity demand using South African data. The paper discusses a comparative analysis of the additive quantile regression model with an extremal mixture model and a nonlinear quantile regression model. The estimated quantiles at each level were then combined using the median approach. The comparisons were carried out using daily peak electricity demand data ranging from January 1997 to May 2014. Proper scoring rules were used to compare the three models, and the model with the smallest score was preferred. The results could be useful to system operators including decision-makers in power utility companies by giving insights and guidance for future electricity demand patterns. The prediction of extremely high quantiles of daily peak electricity demand could help system operators know the possible largest demand that will enable them to supply adequate electricity to consumers and shift demand to off-peak periods. The prediction of extreme conditional quantiles of daily peak electricity demand in the context of South Africa using additive quantile regression, nonlinear quantile regression, and extremal mixture models has not been performed previously to the best of our knowledge.

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“…Application to Real-Life Data. In this section, we illustrate the enhanced and existing methods of estimating tail index under missing observations, on a real-life wind speed data obtained from the extremefit package in R (Durrieu et al[30]). The wind speed data contains the average wind speed in meters per second (m/s) per day in Brest (France) from 1976 to 2005.…”

mentioning

confidence: 99%

An Enhanced Method for Tail Index Estimation under Missingness

Ayiah-Mensah

Minkah

Asiedu

et al. 2021

Journal of Applied Mathematics

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Extreme events in earthquakes, wind speed, among others are rare but may lead to catastrophic effects on humans and the environment. The primary parameter in the estimation of such rare events is the tail index which measures the tail heaviness of an underlying distribution. Since extreme events are rare, the presence of missing observations may further lead to flawed. In view of this, there is a growing effort by researchers to address this problem. However, the existing methods of estimating the tail index use only the available nonmissing data. Thus, if the missing observations are influential values, ignoring them could introduce more bias and higher mean square error (MSE) in the tail index estimation and subsequently other extreme event--estimators such as high quantiles and small exceedance probabilities. In this study, we propose imputation of the missing observations before applying some standard estimators (Hill and geometric-type) to estimate the tail index. Through a simulation study, we assess the performance of the standard estimators under the proposed data enhancement method and the existing modified estimators of the tail index. The results show that the enhanced estimators have relatively lower bias and MSE. The estimation method was illustrated with a practical dataset on wind speed with missing values. Therefore, we recommend imputation mechanism as viable for enhancing the performance of tail index estimators in the case where there is missingness.

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extremefit: A Package for Extreme Quantiles

Cited by 9 publications

References 37 publications

Estimation of Extreme Quantiles of Global Horizontal Irradiance: A Comparative Analysis Using an Extremal Mixture Model and a Generalised Additive Extreme Value Model

Estimation of Extreme Quantiles of Global Horizontal Irradiance: A Comparative Analysis Using an Extremal Mixture Model and a Generalised Additive Extreme Value Model

Prediction of Extreme Conditional Quantiles of Electricity Demand: An Application Using South African Data

An Enhanced Method for Tail Index Estimation under Missingness

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