Date/Time
Date(s) - 18/09/2025
1:30 pm - 2:30 pm

Speaker: Anja Schmiedt (OTH Regensburg)

Location: Hamilton Hall, Room 102

Title: Ordering of random variables via truncation of distributions – application, model, and inference

Abstract: We consider a data set of non-metallic inclusion sizes in samples of engineering steel. Common order statistics are not a suitable model for ascendingly ordered measurements within single samples. To address this issue, a model of ordered random variables from the class of generalized order statistics is proposed, termed ordering via truncation of distributions.

Within this model, the joint maximum likelihood estimation of the model parameters and the shape parameter of an underlying left-truncated Weibull distribution is examined. A model test is also provided where the null hypothesis refers to common order statistics. To reduce the number of model parameters, particularly in small data sets, a link-function approach is studied where the link-function parameter may also serve as a material indicator. Additionally, we propose an asymptotic test to check for the presence of a linear link function, as well as tests concerning its parameters. Furthermore, methods for constructing simultaneous confidence regions for the link function parameters and confidence bands for the entire link function graph are presented.

These methods are applied to a real metallurgical dataset.