2016/04/05 by Cristiano Villa, Villa, Cristiano
Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1604.01268
openalex publication_date 2016/04/05 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In this paper, we discuss a method to define prior distributions for the\nthreshold of a generalised Pareto distribution, in particular when its\napplications are directed to heavy-tailed data. We propose to assign prior\nprobabilities to the order statistics of a given set of observations. In other\nwords, we assume that the threshold coincides to one of the data points. We\nshow two ways of defining a prior: by assigning equal mass to each order\nstatistic, that is a uniform prior, and by considering the worth that every\norder statistic has in representing the true threshold. Both proposed priors\nrepresent a scenario of minimal information, and we study their adequacy\nthrough simulation exercises and by analysing two applications from insurance\nand from finance.\n