A regression model for extreme events and the presence of bimodality with application to energy generation data

Abstract

The application of the theory of extreme values has been growing due to increasing interest in extreme natural events. Many articles on extreme values in data modelling consider unimodal data. This work introduces an appropriate regression for extreme values to detect the presence of bimodality by means of systematic components of two parameters of the odd log‐logistic log‐normal distribution. The global influence is addressed to verify the model robustness and to find possible influential points. Quantile residuals are proposed to detect distribution deficiencies and outliers in the new regression. A real dataset from the electricity generation area is analysed, namely the Santo Antônio Hydroelectric Plant in the state of Rondônia (Brazil), to illustrate the potential of the new regression. The main results indicate that the proposed regression can identify changes in the means and variability of the power generation between extreme events, that is, between the months of June and December.

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“…Recently, some papers on regression models have been published, for example, Hashimoto et al (2019), Prataviera et al (2020), Silva et al (2020) and Vasconcelos et al (2021). In a similar context, we introduce the regression model based on the GOLLGR distribution.…”

An extended Rayleigh model: Properties, regression and COVID-19 application

“…Moreover, g(x) has a vertical asymptotic at x va = [(1/2) − δ]/θ when δ < 1/2, with g(x) < 0 for all x < x va and g(x) > 0 for all x > x va . Since G GR (x; δ, θ) is increasing on (0, ∞), because this one is a cdf, it is plausible to expect that, by varying the parameters, Equation (18) has at most three roots on (0, ∞). So, the pdf of X has at most three critical points on (0, ∞).…”