Construction of asymmetric confidence/uncertainty intervals using semivariance on the example of traffic noise indicators

Abstract

The occurrence of asymmetric probability distributions is quite common. Phenomena such as salary, number of failures, sound level values, etc. have skewed distributions. In such cases, estimating the mean using the interval method can be inaccurate as it ignores the distribution’s asymmetry. Another method of constructing confidence intervals, which does not require symmetry of distributions, is the method based on Chebyshev’s theorem. However, the intervals thus obtained are symmetrical. The approach proposed in this article uses the concept of Chebyshev’s theorem and semivariances to construct new confidence and uncertainty intervals. The article examines the properties of semivariance-based confidence intervals for long-term noise indicators from acoustic monitoring of the city of Gdansk and compares them with classical confidence intervals. The new uncertainty assessment tool proposed in this article in the form of a semivariance-based uncertainty interval can therefore be the basis for new uncertainty assessment methodology and more effective uncertainty.