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

Stępień B.

Archives of Acoustics

2016

Vol. 41, No. 3

517--525

A non-classical model of interval estimation based on the kernel density estimator is presented in this paper. This model has been compared with interval estimation algorithms of the classical (parametric) statistics assuming that the standard deviation of the population is either known or unknown. The non-classical model does not have to assume belonging of random sample to a normal distribution. A theoretical basis of the proposed model is presented as well as an example of calculation process which makes possible determining confidence intervals of the expected value of long-term noise indicators LDEN and LN. The statistical analysis was carried out for 95% interval widths obtained by using each of these models. The inference of their usefulness was performed on the basis of results of non-parametric statistical tests at significance level α = 0.05. The data used to illustrate the proposed solutions and carry out the analysis were results of continuous monitoring of traffic noise recorded in 2004 in one of the main arteries of Kraków in Poland.

Wpływ postaci jądra na wyniki estymacji długookresowych wskaźników hałasu

Stępień B.

Przegląd Mechaniczny

2015

nr 7-8

55--58

W pracy przeanalizowano wpływ funkcji jądrowej na wyniki estymacji wartości oczekiwanej i niepewności standardowej typu A długookresowyctn wskaźników hałasu. Porównano ze sobą kilka podstawowych typów jąder opisanych w literaturze, tj. Epanecznikowa, jednostajne, normalne i trójkątne. Wnioskowanie statystyczne oparto na metodzie porównań wielokrotnych, wykorzystując nieparametryczny test post-hoc Tukeya-Kramera na poziomie istotności a = 0,05.

The effect of kernel function for expected value estimation and type A standard uncertainty of long-term noise indicators was described in this paper. A few basic types of kernel functions presented in the literature i.e. Epanechnikov, uniform, normal, and triangular were compared to each other The statistical inference was based on the multiple comparisons method using the non-parametric post-hoc Tukey-Kramer's test with significance level a = 0,05.

Type A Standard Uncertainty of Long-Term Noise Indicators

Batko W. M., Stępień B.

Archives of Acoustics

2014

Vol. 39, No. 1

25--36

The problem of estimation of the long-term environmental noise hazard indicators and their uncer- tainty is presented in the present paper. The type A standard uncertainty is defined by the standard deviation of the mean. The rules given in the ISO/IEC Guide 98 are used in the calculations. It is usually determined by means of the classic variance estimators, under the following assumptions: the normality of measurements results, adequate sample size, lack of correlation between elements of the sample and observation equivalence. However, such assumptions in relation to the acoustic measurements are rather questionable. This is the reason why the authors indicated the necessity of implementation of non-classical statistical solutions. An estimation idea of seeking density function of long-term noise indicators distri- bution by the kernel density estimation, bootstrap method and Bayesian inference have been formulated. These methods do not generate limitations for form and properties of analyzed statistics. The theoretical basis of the proposed methods is presented in this paper as well as an example of calculation process of expected value and variance of long-term noise indicators LDEN and LN. The illustration of indicated solutions and their usefulness analysis were constant due to monitoring results of traffic noise recorded in Cracow, Poland.