Heavy Tail Distributions

Carmona, René

doi:10.1007/978-1-4614-8788-3_2

Cited by 2 publications

(1 citation statement)

References 56 publications

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“…In these cases, the stopping criteria are specified by the error in the central moments as indicated by the discrepancy between those of the distribution and those resulting from the data generated from the MCS. The error is to be a maximum of 0.1%, as shown by (34), given the first and second central moment of the GEVD (GC 1 and GC 2 ) [65]. Such (35) and (36) are valid for K < 0.5.…”

Section: Monte Carlo Simulationmentioning

confidence: 99%

Stochastic PV model for power system planning applications

Al-Sumaiti

Ahmed

Rivera

et al. 2019

IET Renewable Power Generation

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Planning photovoltaic (PV) power systems integration into the grid necessitates accurate modelling of renewable power generation. Global solar irradiance, weather temperature and PV power losses due to overheating specifically in hot regimes are major factors contributing to PV power generation uncertainty. This study targets demonstrating the effectiveness of deploying advanced five parameter probabilistic distribution 'Wakeby' for modelling PV uncertain power generation, measured as a function of such factors, in power system planning applications. The impact of different approaches for incorporating weather temperature on PV energy estimation is studied. Wakeby-Monte Carlo Simulation for PV power data training with an emphasis on MCS stopping criteria for such advanced distribution is presented. The model is tested and verified in 31-bus distribution system to demonstrate its effectiveness over other literature uncertainty modelling approaches when planning integration of PV systems' integration into the grid to minimise the grid losses cost. Real PV power measurements are utilised as benchmark verifying the accuracy and suitability of the presented uncertainty modelling approach. Simulation results demonstrate a small error of $4.7 in the expected annual cost of grid losses when deploying Wakeby model compared to the benchmark case and that error can vary significantly when deploying other PV models. Γ ω Gamma function of ω α, , , δ, ɛ five parameters of Wakeby distribution K, µ, σ three parameters of general extreme value distribution voltage angle

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Section: Monte Carlo Simulationmentioning

confidence: 99%

Stochastic PV model for power system planning applications

Al-Sumaiti

Ahmed

Rivera

et al. 2019

IET Renewable Power Generation

View full text Add to dashboard Cite

show abstract

Taylor’s law of fluctuation scaling for semivariances and higher moments of heavy-tailed data

Brown

Cohen

Tang

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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We generalize Taylor’s law for the variance of light-tailed distributions to many sample statistics of heavy-tailed distributions with tail index α in (0, 1), which have infinite mean. We show that, as the sample size increases, the sample upper and lower semivariances, the sample higher moments, the skewness, and the kurtosis of a random sample from such a law increase asymptotically in direct proportion to a power of the sample mean. Specifically, the lower sample semivariance asymptotically scales in proportion to the sample mean raised to the power 2, while the upper sample semivariance asymptotically scales in proportion to the sample mean raised to the power (2−α)/(1−α)>2. The local upper sample semivariance (counting only observations that exceed the sample mean) asymptotically scales in proportion to the sample mean raised to the power (2−α2)/(1−α). These and additional scaling laws characterize the asymptotic behavior of commonly used measures of the risk-adjusted performance of investments, such as the Sortino ratio, the Sharpe ratio, the Omega index, the upside potential ratio, and the Farinelli–Tibiletti ratio, when returns follow a heavy-tailed nonnegative distribution. Such power-law scaling relationships are known in ecology as Taylor’s law and in physics as fluctuation scaling. We find the asymptotic distribution and moments of the number of observations exceeding the sample mean. We propose estimators of α based on these scaling laws and the number of observations exceeding the sample mean and compare these estimators with some prior estimators of α.

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Heavy Tail Distributions

Cited by 2 publications

References 56 publications

Stochastic PV model for power system planning applications

Stochastic PV model for power system planning applications

Taylor’s law of fluctuation scaling for semivariances and higher moments of heavy-tailed data

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