Estimating Peaks of Stationary Random Processes: A Peaks-over-Threshold Approach

Model Misspecification in Peaks over Threshold Analysis

Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows the estimation of the marginal distribution of threshold exceedances and of the mean cluster size, but requires the choice of a threshold and of a run paramet...

Wavelet Shrinkage via Peaks over Threshold

Wavelet shrinkage is a non parametric technique used in curve estimation. The idea is to shrink wavelet coefficients towards zero using statistical methods. More specifically, a threshold value is chosen and wavelet coefficients whose absolute values exceed that threshold are kept while others are removed. This has the effect of both reducing the noise contribution and compressing the original ...

Gamma processes and peaks-over-threshold distributions for time-dependent reliability

In the evaluation of structural reliability, a failure is defined as the event in which stress exceeds a resistance that is liable to deterioration. This paper presents a method to combine the two stochastic processes of deteriorating resistance and fluctuating load for computing the time-dependent reliability of a structural component. The deterioration process is modelled as a gamma process, ...

Statistical models for overdispersion in the frequency of peaks over threshold data for a flow series

[1] In a peaks over threshold analysis of a series of river flows, a sufficiently high threshold is used to extract the peaks of independent flood events. This paper reviews existing, and proposes new, statistical models for both the annual counts of such events and the process of event peak times. The most common existing model for the process of event times is a homogeneous Poisson process. T...

Combination of The Peaks - Over - Threshold andBootstrapping Methods for Extreme Value Predi