arXiv subjects

Katarzyna Skowronek

Publications and source records attributed to Katarzyna Skowronek.

3 recordsLinked to original sources

arXiv2026

Testing and estimation of the index of stability of univariate and bivariate symmetric $α-$stable distributions via modified Greenwood statistic

We propose a testing and estimation methodology for univariate and bivariate symmatric $α$-stable distributions using a modified version of the Greenwood statistic. Originally designed for positive-valued random variables, the Greenwood statistic, and its modified version tailored for symmetric distributions, have been predominantly applied to univariate random samples. In this paper, we extend the modified Greenwood statistic to a bivariate setting and examine its probabilistic properties within the class of $α$-stable distributions, with a focus on the sub-Gaussian case. Additionally, we introduce a novel testing approach that considers two variations of the modified Greenwood statistic as test statistics for the bivariate case. In the univariate setting, we adapt the proposed testing methodology for estimating the stability index. The simulation studies presented demonstrate that our proposed methodology outperforms classical approaches previously used in this context and serves as an effective tool for distinguishing between Gaussian and $α$-stable distributions with a stability index close to 2. The theoretical and simulation results are further illustrated with practical data examples.

stat.ME↗

arXiv2024

Modified Greenwood statistic and its application for statistical testing

In this paper, we explore the modified Greenwood statistic, which, in contrast to the classical Greenwood statistic, is properly defined for random samples from any distribution. The classical Greenwood statistic, extensively examined in the existing literature, has found diverse and interesting applications across various domains. Furthermore, numerous modifications to the classical statistic have been proposed. The modified Greenwood statistic, as proposed and discussed in this paper, shares several key properties with its classical counterpart. Emphasizing its stochastic monotonicity within three broad classes of distributions - namely, generalized Pareto, $α-$stable, and Student's t distributions - we advocate for the utilization of the modified Greenwood statistic in testing scenarios. Our exploration encompasses three distinct directions. In the first direction, we employ the modified Greenwood statistic for Gaussian distribution testing. Our empirical results compellingly illustrate that the proposed approach consistently outperforms alternative goodness-of-fit tests documented in the literature, particularly exhibiting superior efficacy for small sample sizes. The second considered problem involves testing the infinite-variance distribution of a given random sample. The last proposition suggests using the modified Greenwood statistic for testing of a given distribution. The presented simulation study strongly supports the efficiency of the proposed approach in the considered problems. Theoretical results and power simulation studies are further validated by real data analysis.

math.ST↗

arXiv2024

Assessment of background noise properties in time and time-frequency domains in the context of vibration-based local damage detection in real environment

Any measurement in condition monitoring applications is associated with disturbing noise. Till now, most of the diagnostic procedures have assumed the Gaussian distribution for the noise. This paper shares a novel perspective to the problem of local damage detection. The acquired vector of observations is considered as an additive mixture of signal of interest (SOI) and noise with strongly non-Gaussian, heavy-tailed properties, that masks the SOI. The distribution properties of the background noise influence the selection of tools used for the signal analysis, particularly for local damage detection. Thus, it is extremely important to recognize and identify possible non-Gaussian behavior of the noise. The problem considered here is more general than the classical goodness-of-fit testing. The paper highlights the important role of variance, as most of the methods for signal analysis are based on the assumption of the finite-variance distribution of the underlying signal. The finite variance assumption is crucial but implicit to most indicators used in condition monitoring, (such as the root-mean-square value, the power spectral density, the kurtosis, the spectral correlation, etc.), in view that infinite variance implies moments higher than 2 are also infinite. The problem is demonstrated based on three popular types of non-Gaussian distributions observed for real vibration signals. We demonstrate how the properties of noise distribution in the time domain may change by its transformations to the time-frequency domain (spectrogram). Additionally, we propose a procedure to check the presence of the infinite-variance of the background noise. Our investigations are illustrated using simulation studies and real vibration signals from various machines.

stat.ME↗