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Viktor Witkovský

Publications and source records attributed to Viktor Witkovský.

5 recordsLinked to original sources
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↗
arXiv2023

Characteristic Function of the Tsallis $q$-Gaussian and Its Applications in Measurement and Metrology

The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the $q$-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, $q$-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent $q$-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent $q$-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions.

stat.CO↗
arXiv2018

Exact distribution of selected multivariate test criteria by numerical inversion of their characteristic functions

Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions. Typically, distribution of many estimators and test statistics can be structurally expressed as a linear combination or product of independent random variables with known distributions and characteristic functions, as is the case for many standard multivariate test criteria. The characteristic function represents complete characterization of the distribution of the random variable. However, analytical inversion of the characteristic function, if possible, frequently leads to a complicated and computationally rather strange expressions for the corresponding distribution function (CDF/PDF) and the required quantiles. As an efficient alternative, here we advocate to use the well-known method based on numerical inversion of the characteristic functions --- a method which is, however, ignored in popular statistical software packages. The applicability of the approach is illustrated by computing the exact distribution of the Bartlett's test statistic for testing homogeneity of variances in several normal populations and the Wilks's $Λ$-distribution used in multivariate hypothesis testing.

stat.CO↗
arXiv2013

Estimation, Testing, and Prediction Regions of the Fixed and Random Effects by Solving the Henderson's Mixed Model Equations

We present a brief overview of the methods for making statistical inference (testing statistical hypotheses, construction of confidence and/or prediction intervals and regions) about linear functions of the fixed effects and/or about the fixed and random effects simultaneously, in conventional simple linear mixed model. The presented approach is based on solutions from the Henderson's mixed model equations.

stat.CO↗