In the study of heavy tail data, several models have been introduced. If the interest is in the tail of the distribution, block maxima or excess over thresholds are the typical approaches, wasting relevant information in the bulk of the data. To avoid this, two building block mixture models for the body (below the threshold) and the tail (above the threshold) are proposed. In this paper, we exploit the richness of nonparametric mixture models to model heavy tail data. We specifically consider mixtures of shifted gamma-gamma distributions with four parameters and a normalised stable processes as a mixing distribution. One of these parameters is associated with the tail. By studying the posterior distribution of the tail parameter, we are able to estimate the proportion of the data that supports a heavy tail component. We develop an efficient MCMC method with adapting Metropolis-Hastings steps to obtain posterior inference and illustrate with simulated and real datasets.

翻译：在重尾数据研究中，已有多种模型被提出。若关注分布尾部特征，通常采用块极大值或超阈值方法，但这会损失数据主体部分的重要信息。为避免此问题，本文提出针对主体（阈值以下）和尾部（阈值以上）的双模块混合模型。本研究利用非参数混合模型的丰富表达能力对重尾数据进行建模，特别采用四参数移位伽马-伽马分布混合模型，并以归一化稳定过程作为混合分布。其中一个参数与尾部特征相关。通过研究尾部参数的后验分布，我们能够估计支持重尾成分的数据比例。本文开发了具有自适应Metropolis-Hastings步骤的高效MCMC方法以获得后验推断，并通过模拟和真实数据集进行了验证。