Gejza Wimmer | Searcharxiv

arXiv2025

Calibration of Scanning Thermal Microscope using Optimal Estimation of Function Parameters by Iterated Linearization

Scanning thermal microscopy is a unique tool for the study of thermal properties at the nanoscale. However, calibration of the method is a crucial problem. When analyzing local thermal conductivity, direct calibration is not possible and reference samples are used instead. As the calibration dependence is non-linear and there are only a few calibration points, this represents a metrological challenge that needs complex data processing. In this contribution we present use of the OEFPIL algorithm for robust and single-step evaluation of local thermal conductivities and their uncertainties, simplifying this procedure. Furthermore, we test the suitability of SThM calibration for automated measurement.

physics.data-an↗

arXiv2017

Computing the aggregate loss distribution based on numerical inversion of the compound empirical characteristic function of frequency and severity

A non-parametric method for evaluation of the aggregate loss distribution (ALD) by combining and numerically inverting the empirical characteristic functions (CFs) is presented and illustrated. This approach to evaluate ALD is based on purely non-parametric considerations, i.e., based on the empirical CFs of frequency and severity of the claims in the actuarial risk applications. This approach can be, however, naturally generalized to a more complex semi-parametric modeling approach, e.g., by incorporating the generalized Pareto distribution fit of the severity distribution heavy tails, and/or by considering the weighted mixture of the parametric CFs (used to model the expert knowledge) and the empirical CFs (used to incorporate the knowledge based on the historical data - internal and/or external). Here we present a simple and yet efficient method and algorithms for numerical inversion of the CF, suitable for evaluation of the ALDs and the associated measures of interest important for applications, as, e.g., the value at risk (VaR). The presented approach is based on combination of the Gil-Pelaez inversion formulae for deriving the probability distribution (PDF and CDF) from the compound (empirical) CF and the trapezoidal rule used for numerical integration. The applicability of the suggested approach is illustrated by analysis of a well know insurance dataset, the Danish fire loss data.

stat.CO↗

arXiv2014

Logarithmic Lambert $\mathrm{W}\times {\cal F}$ random variables for the family of chi-squared distributions and their applications

We introduce a class of logarithmic Lambert W random variables for a specific family of distributions. In particular, we characterize the log-Lambert W random variables for chi-squared distributions which naturally appear in the likelihood based inference of normal random variables.

math.ST↗