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Skewed probability distributions are important when modeling skewed data sets because they provide a way to describe the shape of the distribution and estimate the likelihood of extreme events. Asymmetric probability distributions have the potential to handle and assess problems in actuarial risk assessment and analysis. To that end, we present a new right-skewed one-parameter distribution. In this work and for this purpose, a right-skewed probability distribution was derived and analyzed. The new distribution outperformed the exponential distribution, the Pareto distribution, the Chen distribution, and others in the field of actuarial risk analysis. Some useful key risk indicators are considered and analyzed to analyze the risks and for comparison with the competitive model. Several actuarial risk functions and indicators are evaluated and analyzed using the U.K. insurance claims data set. The process of risk assessment and analysis was carried out using a comprehensive simulation. For the purposes of distributional validity, a modified chi-squared type test is presented and employed in the testing process. The new, modified chi-squared type test that is used is simply an extension of the Rao–Robson–Nikulin test. In this work, the distributional validity is presented and analyzed under right-skewed censored and uncensored data sets. [ABSTRACT FROM AUTHOR]

Extreme sea level estimates are fundamental for mitigating coastal flooding as they provide insight for defence engineering. As the global climate changes, rising sea levels combined with increases in storm intensity and frequency pose an increasing risk to coastline communities. We present a new method for estimating extreme sea levels that accounts for the effects of climate change on extreme events that are not accounted for by mean sea level trends. We follow a joint probabilities methodology, considering skew surge and peak tides as the only components of sea levels. We model extreme skew surges using a non-stationary generalised Pareto distribution (GPD) with covariates accounting for climate change, seasonality and skew surge–peak tide interaction. We develop methods to efficiently test for extreme skew surge trends across different coastlines and seasons. We illustrate our methods using data from four UK tide gauges and estimate sea level return levels when accounting for these long-term trends. [ABSTRACT FROM AUTHOR]

Due to the growing proportion of wind energy in Great Britain's energy mix, prolonged periods of low wind power generation have become a significant challenge for decarbonising the electricity system. As such, characterising drought severity and duration is important for ensuring the reliability of the electricity system. Employing concepts derived from hydrology, an extreme value analysis was carried out on wind drought events in Great Britain based on 72 years of ERA5 reanalysis data. The application of pooling procedures was found to be beneficial in robustly identifying wind droughts in cases where the capacity factor is not constantly below an arbitrary threshold. The sequent peak algorithm pooling was found to have particular relevance for electricity systems where energy storage technologies are used to compensate for low wind power generation. The Pearson-III distribution was identified as a suitable model to represent extreme wind droughts, while the Lognormal and Generalised Pareto distributions are also viable alternatives. Sustained periods of low wind power generation with a duration of 14 days were estimated to have a return period of five years and the longest event on record of approximately 26 days is expected to occur once every 100 years. The investigation of these wind droughts from a hydrological perspective has thus shown that they may not be particularly rare occurrences. • Pooling methods can characterise wind droughts as periods of overall low energy generation. • Sequent Peak Algorithm is able to identify the longest wind droughts. • Pearson-III distribution is a suitable model for representing extreme wind droughts. • Wind droughts lasting two weeks are estimated to have a return period of five years. [ABSTRACT FROM AUTHOR]

Recent flooding related to extreme precipitation in the UK has highlighted the importance of better understanding these events. Many studies have quantified annual exceedance probabilities (or return periods) for UK extreme daily precipitation using fixed regions (e.g., HadUKP) and region of interest (ROI) (e.g., Flood Estimation Handbook) approaches, although fewer have evaluated short‐duration events, which are important for flash flooding. Existing UK extreme precipitation regions are based on daily datasets which have different characteristics compared to sub‐daily extremes, and their application to quantify short‐duration extremes may therefore be inappropriate. We use a recently available, quality‐controlled hourly precipitation dataset for the UK from 1992 to 2014 to derive various extreme precipitation indices (e.g., annual maxima, 0.99 quantile) which are combined with additional climatological variables (e.g., temperature), geographical characteristics (e.g., latitude), and weather patterns (WPs) to characterize the UK hourly extreme precipitation climatology and to define five new hourly extreme regions. These regions fulfil regional homogeneity and discordancy statistical measures, and reflect the dynamical processes associated with the weather pattern categorisation defined over the UK and surrounding European area. Thereafter, we use regional frequency analysis (RFA) to fit generalized extreme value (GEV) and generalized Pareto (GP) distributions to 1 hr annual maxima (AMAX) and 0.99 quantile (Q99) precipitation, respectively, to calculate regional annual probability estimates (AEP) for 20%, 10%, and 2% (i.e., 5‐, 10‐, and 50‐year return periods). The new regions capture the spatial variation of hourly precipitation across the UK. Furthermore, the AEP estimates using both distributions are similar for each region. Finally, the WPs associated with the frequency and intensity of the most extreme hourly precipitation accumulations are not identical to results reported by others for daily precipitation. [ABSTRACT FROM AUTHOR]

Summary: There is a propensity for an extreme value analysis to be conducted as a consequence of a large flooding event. This timing of the analysis introduces bias and poor coverage probabilities into the associated risk assessments and leads subsequently to inefficient flood protection schemes. We explore these problems through studying stochastic stopping criteria and propose new likelihood‐based inferences that mitigate against these difficulties. Our methods are illustrated through the analysis of the river Lune, following its experiencing the UK's largest ever measured flow event in 2015. We show that without accounting for this stopping feature there would be substantial overdesign in response to the event. [ABSTRACT FROM AUTHOR]

Household survey data provide a rich information set on income, household context and demographic variables, but tend to underreport incomes at the very top of the distribution. Administrative data like tax records offer more precise information on top incomes, but at the expense of household context details and incomes of non-filers at the bottom of the distribution. We combine the benefits of the two data sources and develop an integrated approach for top-corrected income distributions where we impute top incomes in survey data using information on top income distribution from tax data. We apply our approach to European EU-SILC survey data which in some countries include administrative data. We find higher inequality in those European countries that exclusively rely (Germany, UK) or have relied (Spain) on interviews for the provision of EU-SILC survey data as compared to countries that use administrative data. [ABSTRACT FROM AUTHOR]

One of the major concerns in Flood Frequency Analysis (FFA) is to predict floods of high magnitude for larger return periods. Magnitudes of smaller floods behave as nuisance in the estimation of larger floods. In this study, to avoid the unnecessary effect due to smaller observations, we implemented the technique of left censoring. The primary objective of this study is to see the efficacy of censoring, by comparing Regional Flood Frequency Analysis (RFFA) using Partial Linear Moments (PLM) for censored samples with RFFA using Linear Moments (LM) for uncensored samples of annual peak flows observed at ten stations of Indus Basin in Pakistan. After fulfillment of fundamental assumptions of randomness, independence, homogeneity, and stationarity, a Grubbs-Beck (GB) test for outlier detection is applied to the samples from all stations. For further analysis, Discordancy measure shows that none of the site is discordant and all ten stations would be retained for further investigation. On the basis of geographical closeness, stream hydrology and morphology of Indus basin, a single homogenous region is proposed and testified by the heterogeneity standards. The best fit distribution is selected by implying the Z-statistic (goodness of fit test base on LM) and L-Moments Ratio Diagram (LMRD). Generalized Pareto Distribution (GPA) distribution under PLM while Generalized Normal Distribution (GNO) under LM is selected as the reasonable choice for design flood estimation. Monte Carlo simulation experiment is performed to check the efficacy of PLM over LM through Root Means Square Error (RMSE) and bias. These accuracy measures indicated the outperformance of censored samples under PLM to uncensored samples under LM. [ABSTRACT FROM AUTHOR]

When assessing the impact of extreme events, it is often not just a single component, but the combined behavior of several components which is important. Statistical modeling using multivariate generalized Pareto (GP) distributions constitutes the multivariate analogue of univariate peaks over thresholds modeling, which is widely used in finance and engineering. We develop general methods for construction of multivariate GP distributions and use them to create a variety of new statistical models. A censored likelihood procedure is proposed to make inference on these models, together with a threshold selection procedure, goodness-of-fit diagnostics, and a computationally tractable strategy for model selection. The models are fitted to returns of stock prices of four UK-based banks and to rainfall data in the context of landslide risk estimation. Supplementary materials and codes are available online. [ABSTRACT FROM AUTHOR]

For the first time, an extreme value analysis of electricity demand in the UK is provided. The analysis is based on the generalized Pareto distribution. Its parameters are allowed to vary linearly and sinusoidally with respect to time to capture patterns in the electricity demand data. The models are shown to give reasonable fits. Some useful predictions are given for the value at risk of the returns of electricity demand. [ABSTRACT FROM AUTHOR]

Recent changes in the distribution of income need to be placed in historical context. The paper provides new evidence about the evolution of top incomes in the UK over the 20th century. Making use of published tabulations of the income tax statistics, and of microdata for recent years, we construct estimates of the shares of top income groups, giving for the first time an annual time series for gross incomes that spans more than 90 years. The paper pays particular attention to the problems of data construction and of the interpretation of tax-based evidence. The resulting statistics have evident limitations but throw light on periods, such as that between the First and Second World Wars, for which there is little other empirical material. The results bring out clearly how the major equalization of the first three-quarters of the century in the UK has been reversed, taking the shares of the top income groups back to levels of inequality found 50 years ago. A similar U-shaped pattern is found for the USA, but the post-war experience of France is different from that in the UK. [ABSTRACT FROM AUTHOR]

A simple and effective lattice–gas–automaton (LGA) economic model is proposed for the income distribution. It consists of four stages: random propagation, economic transaction, income tax, and charity. Two types of discrete models are introduced: two-dimensional four-neighbor model (D2N4) and D2N8. For the former, an agent either remains motionless or travels to one of its four neighboring empty sites randomly. For the latter, the agent may travel to one of its nearest four sites or the four diagonal sites. Afterwards, an economic transaction takes place randomly when two agents are located in the nearest (plus the diagonal) neighboring sites for the D2N4 (D2N8). During the exchange, the Matthew effect could be taken into account in the way that the rich own a higher probability of earning money than the poor. Moreover, two kinds of income tax models are incorporated. One is the detailed taxable income brackets and rates, and the other is a simplified tax model based on a fitting power function. Meanwhile, charity is considered with the assumption that a richer agent donates a part of his income to charity with a certain probability. Finally, the LGA economic model is validated by using two kinds of benchmarks. One is the income distributions of individual agents and two-earner families in a free market. The other is the shares of total income in the USA and UK, respectively. Besides, impacts of the Matthew effect, income tax and charity upon the redistribution of income are investigated. It is confirmed that the model has the potential to offer valuable references for formulating financial laws and regulations. [ABSTRACT FROM AUTHOR]

• The choice of estimators has an impact on the selected thresholds. • The proposed automated method based on threshold stability gives robust estimates. • It results in the highest agreement between simulated and empirical quantiles. • The modelled hourly peak flow is consistently closer to the empirical one. This study investigated core components of an extreme value methodology for the estimation of high-flow frequencies from agricultural surface water run-off. The Generalized Pareto distribution (GPD) was used to model excesses in time-series data that resulted from the 'Peaks Over Threshold' (POT) method. First, the performance of eight different GPD parameter estimators was evaluated through a Monte Carlo experiment. Second, building on the estimator comparison, two existing automated GPD threshold selection methods were evaluated against a proposed approach that automates the threshold stability plots. For this second experiment, methods were applied to discharge measured at a highly-instrumented agricultural research facility in the UK. By averaging fine-resolution 15-minute data to hourly, 6-hourly and daily scales, we were also able to determine the effect of scale on threshold selection, as well as the performance of each method. The results demonstrate the advantages of the proposed threshold selection method over two commonly applied methods, while at the same time providing useful insights into the effect of the choice of the scale of measurement on threshold selection. The results can be generalised to similar water monitoring schemes and are important for improved characterisations of flood events and the design of associated disaster management protocols. [ABSTRACT FROM AUTHOR]

Under the influence of local‐ and large‐scale climatological processes, extreme river flow events often show long‐term trends, seasonality, interyear variability, and other characteristics of temporal nonstationarity. Properly accounting for this nonstationarity is vital for making accurate predictions of future floods. In this paper, a regional model based on the generalised Pareto distribution is developed for peaks‐over‐threshold river flow data sets when the event sizes are nonstationary. If observations are nonstationary and covariates are available, then extreme‐value (semi)parametric regression models may be used. Unfortunately, the necessary covariates are rarely observed, and if they are, it is often not clear which process, or combination of processes, to include in the model. Within the statistical literature, latent process (or random effects) models are often used in such scenarios. We develop a regional time‐varying random effects model that allows identification of temporal nonstationarity in event sizes by pooling information across all sites in a spatially homogeneous region. The proposed model, which is an instance of a Bayesian hierarchical model, can be used to predict both unconditional extreme events such as the m‐year maximum and extreme events that condition on being in a given year. The estimated random effects may also tell us about likely candidates for the climatological processes that cause nonstationarity in the flood process. The model is applied to UK flood data from 817 stations spread across 81 hydrometric regions. [ABSTRACT FROM AUTHOR]