Ayana Mateus

The tail of a probability distribution captures important information about the magnitude and frequency of extreme events. Thus, understanding the tail behavior is crucial in decision making and risk assessment. Statistical analysis and predictions of extreme events often require the estimation of the extreme value index, a key parameter that describes the tail heaviness. We present a new class of estimators of a positive extreme value index, based on probability weighted moment method, a flexible framework for tail inference. The asymptotic normality of the introduced class of estimators is established, and a comparison with the Hill estimator is also provided. The effectiveness of the proposed class of estimators is demonstrated through both simulation studies and a real data application, highlighting their potential in extreme value analysis.

Estimation based on probability-weighted moments is a well-established method and an excellent alternative to the classic method of moments or the maximum likelihood method, especially for small sample sizes. In this research, we developed a new class of estimators for the parameters of the Pareto type I distribution. A generalization of the probability-weighted moments approach is the foundation for this new class of estimators. It has the advantage of being valid in the entire parameter space of the Pareto distribution. We established the asymptotic normality of the new estimators and applied them to simulated and real datasets in order to illustrate their finite sample behavior. The results of comparisons with the most used estimation methods were also analyzed.

The log-logistic distribution is widely used in different fields of study such as survival analysis, hydrology, insurance, and economics. Recently, Ahsanullah and Alzaatreh studied the best linear unbiased estimators for the location and the scale parameters of the three-parameter log-logistic model. The same authors also propose a shift-invariant Hill estimator for the unknown shape parameter. In this work, we propose a new estimation method for the shape parameter. We derive its nondegenerate asymptotic behaviour and analyse its finite sample performance through a Monte Carlo simulation study. To have precise estimates, we present a method for selecting the threshold. To illustrate the improvement achieved, efficiency comparisons are also provided.

In this paper we revisit the Jackson exponentiality test. We study and provide functions in R language to compute theoretical moments, the distribution function and quantiles of the statistic test. Approximations to the exact distribution function and quantiles are also provided and their precision discussed. In addition, we provide an application of the Jackson test to real data.

Floods are recurrent events that can have a catastrophic impact. In this work we are interested in the analysis of a data set of gauged daily flows from the Whiteadder Water river, Scotland. Using statistic techniques based on extreme value theory, we estimate several extreme value parameters, including extreme quantiles and return periods of high levels.