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On tails of symmetric and totally asymmetric alpha-stable distributions

Bednorz Witold M., Łochowski Rafał M., Martynek Rafał

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 2

321--345

We estimate up to universal constants tails of symmetric and to-tally asymmetric 1-dimensional α-stable distributions in terms of functions of the parameters of these distributions. In particular, for values of α close to 2we specify where exactly the tail changes from being Gaussian and starts to behave like in the Pareto distribution.

Multifractal Nature of Diesel Engine Rattle Noise in Vehicle

Puchalski A., Komorska I.

Archives of Acoustics

2017

Vol. 42, No. 3

469--474

The investigation results of the emission of noises accompanying the diesel engine powertrain running in unloaded condition at low or idle speed, are presented in the hereby paper. The multifractal nature of the tested signals was confirmed by means of two groups of parameters. The proposed local parameters are based on the distribution of the probability density of measures, segregated into subsets according to pointwise Holder exponents. The obtained spectra constitute a set of multifractal measures related to singularities representing the local scaling of measures in various points of the time series. Global parameters were defined on the basis of multifractal measures of the parametrised Renyi’s entropy. These are properties treating summarily the whole spectrum of the emitted noise and reflecting changes of the vibroacoustic energy levels generated by noise sources. The tests encompassing simultaneous application of both groups of parameters confirmed their efficiency in the comparative analysis as well as in the subjective assessment of the noise level generated in the drive system of vehicles with diesel engines. This opens new possibilities within the simulation range of vehicle noises, for the needs of constructing the passive and active reduction systems of the effects of the vibroacoustic energy propagation.