Comparison of some Bayesian estimation methods for type-I generalized extreme value distribution with simulation

Habeeb, Sundos Bader; Abdullah, Fatima K.; Shalan, Rehab Noori; Hassan, Amal S.; Almetwally, Ehab M.; Alghamdi, Fatimah M.; Alsheikh, Sara Mohamed Ahmed; Hossain, Md Moyazzem

doi:10.1016/j.aej.2024.04.042

Cited by 2 publications

(1 citation statement)

References 37 publications

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“…8 where the goodness of fit observed. For the effect of lower and upper points to the value of support the next approximation from calculus follows: The central estimation for the worst-case scenario of daily hourly loads is approximately Min=9GW, Max=12GW and is the heaviest daily task expected from GEV analysis [86][87][88][89][90][91][92][93][94][95]. Next is a challenge to find the specific number of days for return level and current time by using an optimization method.…”

Section: Extreme Value Analysismentioning

confidence: 99%

Electricity Demand, Forecasting the Peaks: Development and Implementation of C-EVA Method

Theodorou,

Christopoulos

2024

GLCE

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Price spikes in electricity markets are very frequent, posing tremendous burden on household income and on manufacturing cost. Electricity demand (load) can be divided in two parts, energy (MWh) and peak (MW) and most of time peak is responsible for the price spikes. Literature review while devoting most of the discussion to energy, lags in the investigation of peak. In this research, a model for peak demand analysis and forecasting is developed. The model is based on a portfolio of cluster and extreme value analysis (C-EVA) methods using UIK, EDE and WSL innovations for the optimal determination of clusters and the daily peaks divulgence. C-EVA method consists of the Clustering part for optimal number of clusters determination and classification of day and month of peak, and the part of Extreme Value Analysis for computation of the statistical confidence interval for the load maxima. C-EVA after using all the currently available load maxima, estimates statistically the expected worst-case scenario for peaks of loads. Load peaks will be determined by EVA based on an estimated bimodal distribution while a signaling method will prompt the probability of extremes. The added value of the proposed method is that does not reject the extreme values as most methodologies do. Extreme Value Analysis for maxima and minima provide estimators for highest and lowest expected hourly load, while giving the confidence interval of the return level using an optimization method for the selection of a rolling time window, as the return period. It was found that distributed generation of renewables create a camel effect on the load peaks which increases sharpness. The proposed methodology solved this issue while opening the ground for future research for the role of storage, batteries as well as for virtual power plants as an integrated portfolio of renewables generation.

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Section: Extreme Value Analysismentioning

confidence: 99%

Electricity Demand, Forecasting the Peaks: Development and Implementation of C-EVA Method

Theodorou,

Christopoulos

2024

GLCE

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Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test

Gong,

Yin

2024

PLoS ONE

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This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate `estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data.

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Comparison of some Bayesian estimation methods for type-I generalized extreme value distribution with simulation

Cited by 2 publications

References 37 publications

Electricity Demand, Forecasting the Peaks: Development and Implementation of C-EVA Method

Electricity Demand, Forecasting the Peaks: Development and Implementation of C-EVA Method

Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test

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