Upper record values from the generalized Pareto distribution and associated statistical inference.

We investigate point estimation and confidence interval estimation for the heavy-tailed generalized Pareto distribution (GPD) based on the upper record values. When the shape parameter is known, the bias-corrected moments estimators and maximum likelihood estimators (MLE) for the location and scale parameters are derived. However, in practice, the shape parameter is typically unknown. We propose the MLE by a new methodological approach for all three parameters of the heavy-tailed GPD when the shape parameter is unknown. Confidence intervals for the location and scale parameters are constructed by the equal probability density principle. If the shape parameter is known, we can find known distributions of the pivots of the location and scale parameters, but not approximate. While if the shape parameter is unknown, the distributions of the pivots are closed linked to an estimation of the shape parameter. The advantage of our method is that the proposed interval estimation provides the smallest confidence interval, regardless of whether the distribution of the pivot is symmetric. Extensive simulations are used to demonstrate the performance of the point estimation and confidence intervals estimation and show that our method outperforms the traditional technique in most cases. [ABSTRACT FROM AUTHOR]