Random Distribution of Long-Term Indicators of Variable Emission Conditions

Abstract

This study is dedicated to the problem of estimating uncertainties of long-term noise indicators, when differences in the sound level emission at various time periods of the calendar year are taken into consideration. This task is defined by referring their influence values -in the determined time intervals -to the year period. Due to the limited possibilities of a total monitoring of parameters necessary for the precise estimation of the long-term sound levels, this estimation process is often limited (in accordance with the EU environmental recommendations) to two condition classes. They are defined by two sound levels occurring with probabilities (frequencies) p and 1 − p, in the analyzed reference period. In this paper we present a method of calculating uncertainties of this procedure assuming that frequency of determined events are known. The probability distribution for the estimated value was assessed. The developed model formalism of the estimation of uncertainties of long-term sound levels together with algorithms assigned to it, was analyzed. The proposed solution was illustrated by examples of uncertainty calculations of the averaged sound levels in acoustic assessments of environmental hazards.

Verification of the Calculation Assumptions Applied to Solutions of the Acoustic Measurements Uncertainty

“…They are connecting these tests with the results of the central limiting Lindeberg-Levy theorem, determining the convergent form of random events distribution, not analysing a mechanism of the sound level measurement result generation. As it is shown in papers (Batko, Przysucha, 2010;2011;2012), taking into account this mechanism leads to distributions considerably differing from the normal distribution.…”

“…Unacceptability of the assumption of the possibility of approximating the acoustic measurements results by the normal distribution, can be also a reason for wider searching for the proper analytical form of the density probability distribution function for the controlled noise indicators mentioned in papers (Batko, Przysucha, 2010;2011;2012). This form is related to the propagation law of the density distribution function of the control process input variables and to the distribution of the output value of the estimated indicator in the noise indicator control process.…”

Confidence Intervals for the Long-Term Noise Indicators Using the Kernel Density Estimator

“…f (x) n h^K ' i=1 h ( 7 ) for x = x i,i = 1 ,... ,n. The kernel function K (•) rep resents how the probability mass is assigned, so for the histogram, it is just a constant in any particular interval. This function controls the shape.…”

Bootstrap Confidence Intervals for Noise Indicators

“…Additionally,Wszołek and Kłaczyński [11] provedt hat the road trafficn oise probability distributions are not related to anystatistical distribution known in the literature. However, the probability density function of the average long-term sound levels shows some asymmetry [12].…”