A trial of generalizing discrete and continuous type probability expressions due to Kurze for road traffic noise.

Abstract

Until the present, various expressions of a probability distribution function, which play an important role in the evaluation of road traffic noise, have been presented. We firstly derive a new universal expansion expression of multivariate joint probability distribution with both discrete and continuous random variables, based on the Lebesgue's decomposition theorem. We show that our expressions, as special cases, agree with Kurze's probability expressions introduced for the road traffic noise such as “semiinfinite source line, ” “short source line” and “very light traffic.” As one example, after choosing a combination form of Gaussian and gamma distribution functions as the first term of our expansion expression, we confirm experimentally the validity and the effectiveness of our theory not only by means of a digital simulation technique but also by applying to actually observed road traffic noise data.