In the parameter estimation of limit extreme value distributions, most employed methods only use some of the available data. Using the peaks-over-threshold method for Generalized Pareto Distribution (GPD), only the observations above a certain threshold are considered; therefore, a big amount of information is wasted. The aim of this work is to make the most of the information provided by the observations in order to improve the accuracy of Bayesian parameter estimation. We present two new Bayesian methods to estimate the parameters of the GPD, taking into account the whole data set from the baseline distribution and the existing relations between the baseline and the limit GPD parameters in order to define highly informative priors. We make a comparison between the Bayesian Metropolis–Hastings algorithm with data over the threshold and the new methods when the baseline distribution is a stable distribution, whose properties assure we can reduce the problem to study standard distributions and also allow us to propose new estimators for the parameters of the tail distribution. Specifically, three cases of stable distributions were considered: Normal, Lévy and Cauchy distributions, as main examples of the different behaviors of the tails of a distribution. Nevertheless, the methods would be applicable to many other baseline distributions through finding relations between baseline and GPD parameters via studies of simulations. To illustrate this situation, we study the application of the methods with real data of air pollution in Badajoz (Spain), whose baseline distribution fits a Gamma, and show that the baseline methods improve estimates compared to the Bayesian Metropolis–Hastings algorithm.

A Bayesian hierarchical framework with a Gaussian copula and a generalized extreme value (GEV) marginal distribution is proposed for the description of spatial dependencies in data. This spatial copula model was applied to extreme summer temperatures over the Extremadura Region, in the southwest of Spain, during the period 1980–2015, and compared with the spatial noncopula model. The Bayesian hierarchical model was implemented with a Monte Carlo Markov Chain (MCMC) method that allows the distribution of the model’s parameters to be estimated. The results show the GEV distribution’s shape parameter to take constant negative values, the location parameter to be altitude dependent, and the scale parameter values to be concentrated around the same value throughout the region. Further, the spatial copula model chosen presents lower deviance information criterion (DIC) values when spatial distributions are assumed for the GEV distribution’s location and scale parameters than when the scale parameter is taken to be constant over the region.

Value at Risk (VaR) and Conditional Value at Risk (CVaR) have become the most popular measures of market risk in Financial and Insurance fields. However, the estimation of both risk measures is challenging, because it requires the knowledge of the tail of the distribution. Therefore, Extreme Value Theory initially seemed to be one of the best tools for this kind of problems, because using peaks-over-threshold method, we can assume the tail data approximately follow a Generalized Pareto distribution (GPD). The main objection to its use is that it only employs observations over the threshold, which are usually scarce. With the aim of improving the inference process, we propose a new Bayesian method that computes estimates built with all the information available. Informative prior Bayesian (IPB) method employs the existing relations between the parameters of the loss distribution and the parameters of the GPD that models the tail data to define informative priors in order to perform Metropolis–Hastings algorithm. We show how to apply IPB when the distribution of the observations is Exponential, stable or Gamma, to make inference and predictions. .Afterwards, we perform a thorough simulation study to compare the accuracy and precision of the estimates computed by IPB and the most employed methods to estimate VaR and CVaR. Results show that IPB provides the most accurate, precise and least biased estimates, especially when there are very few tail data. Finally, data from two real examples are analysed to show the practical application of the method.

The entertainment industry undergoes constant changes, and video games, along with the ways people enjoy them, evolve dynamically. In this context, there arises a need to innovate in areas such as user–game interaction and the design of conventional controllers to keep up with these transformations. This study has found that the design requirements of the external geometry of video game controllers significantly impact users’ purchasing decisions, who often rely on their sensations and emotions. The primary aim of this research has been to demonstrate that it is possible to develop a specific methodology to establish design guidelines that evaluate geometry and ergonomic aspects, considering users’ emotional needs. To achieve this goal, the Kansei methodology has been employed, an engineering discipline that focuses on product design based on emotional interaction and user sensations when using them. Through advanced statistical techniques such as principal component analysis and linear regression, the set of observations has been reduced and a robust predictive model has been developed. Following this methodological approach, surveys and field studies have been conducted, thus differentiating the project from a conventional engineering approach in various stages. Special attention has been paid to the tactile part of the controller, especially its casing. After thorough analysis, the redesigned casing, incorporating improvements derived from statistical analyses, has been compared to existing market models. The results obtained show a significant improvement compared to existing market models, particularly highlighting enhancements in functional characteristics and ergonomic design, enabling comfortable use for individuals with different hand sizes and preventing the grip surface from being slippery. In summary, this work supports the effectiveness of the Kansei methodology as an approach to adapting product design to users’ perceptions and emotional needs.

Usual estimation methods for the parameters of extreme value distributions only employ a small part of the observation values. When block maxima values are considered, many data are discarded, and therefore a lot of information is wasted. We develop a model to seize the whole data available in an extreme value framework. The key is to take advantage of the existing relation between the baseline parameters and the parameters of the block maxima distribution. We propose two methods to perform Bayesian estimation. Baseline distribution method (BDM) consists in computing estimations for the baseline parameters with all the data, and then making a transformation to compute estimations for the block maxima parameters. Improved baseline method (IBDM) is a refinement of the initial idea, with the aim of assigning more importance to the block maxima data than to the baseline values, performed by applying BDM to develop an improved prior distribution. We compare empirically these new methods with the Standard Bayesian analysis with non-informative prior, considering three baseline distributions that lead to a Gumbel extreme distribution, namely Gumbel, Exponential and Normal, by a broad simulation study.

A statistical study was made of the summer extreme temperatures over peninsular Spain in the last forty years. Records from 158 observatories regularly distributed over Iberia with no missing data were available for the common period from 1981 to 2020. For this purpose, a hierarchical spatio-temporal model with a Gaussian copula and a generalized extreme value parametrization of the extreme events was used. The temporal trend in maximum extreme temperatures was studied making use of both a stationary model and a nonstationary one that takes into account the influence of anthropogenic climate change on extreme temperatures using the global mean temperature as a function of time for the study period. The results led to a better fit of the nonstationary model, with there being a 3.5-fold greater increase in the 20-year return level of the extreme temperatures than in that corresponding to the global mean temperature.