Hostname: page-component-5c6d5d7d68-wpx84 Total loading time: 0 Render date: 2024-08-20T12:15:43.244Z Has data issue: false hasContentIssue false
  • English
  • Français

Some exact distributions in traffic noise theory

Published online by Cambridge University Press:  01 July 2016

Allan H. Marcus
Allan H. Marcus*
Affiliation:
University of Maryland, Baltimore County
Get access Rights & Permissions [Opens in a new window]

Abstract

The moment-generating function of the traffic noise from a stream of vehicles with identical noise emissions cannot be readily inverted. If the emissions are not equal, this generating function can be inverted to obtain the exact form of the distribution function in some particular cases. Noise intensity has a maximally skew stable distribution with exponent 1/2 for observers on the highway, whatever the distribution of emissions. The distribution at any distance from the highway is an exponentially modified stable law with exponent 1/2 for an improper exponential distribution of emissions, and an infinite series involving this stable law and iterated error functions when emissions have an exponential distribution. A doubly stochastic process for emissions produces distributions of traffic noise intensity in the domain of attraction of skew stable laws with exponent α, 1/2 < α < 2. The inverse Gaussian (exponentially modified skew stable law with exponent 1/2) is recommended as the best choice of a two-parameter family for fitting traffic noise intensity distributions.

Keywords

TRAFFIC NOISESHOT NOISEINVERSE GAUSSIAN DISTRIBUTIONSTABLE LAWLOG-NORMAL DISTRIBUTIONFILTERED POISSON PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 3 , September 1975 , pp. 593 - 606
Copyright
Copyright © Applied Probability Trust 1975 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Abramowitz, M. and Stegun, I. A. (1964) Handbook of Mathematical Functions (HMF). National Bureau of Standards, Applied Math. Series 55.Google Scholar
[2] Bolshev, L. M., Zolotarev, V. M., Kedrova, E. S. and Rybinskaya, M. A. (1972) Tables of cumulative functions of one-sided stable distributions. SIAM J. Theory of Probability 15, 299–309.Google Scholar
[3] Chhikara, R. S. and Folks, J. L. (1974) Estimation of the inverse Gaussian distribution function J. Amer. Statist. Assoc. 69, 250–255.CrossRefGoogle Scholar
[4] Kurze, U. J. (1971a) Statistics of road traffic noise. J. Sound and Vibration 18, 171–195.CrossRefGoogle Scholar
[5] Kurze, U. J. (1971b) Noise from complex road traffic. J. Sound and Vibration 19, 167–177.CrossRefGoogle Scholar
[6] Kurze, U. J. (1974) Frequency curves of road traffic noise. J. Sound and Vibration 33, 171–185.Google Scholar
[7] Lewis, P. T. (1973) The noise generated by single vehicles in freely flowing traffic. J. Sound and Vibration 30, 191–206.Google Scholar
[8] Marcus, A. H. (1973) Traffic noise as a filtered Markov renewal process. J. Appl. Prob. 10, 377–386.Google Scholar
[9] Marcus, A. H. (1974) Statistical aspects of highway noise-data, simulation, models. University of Maryland Baltimore County Research Report (revised).Google Scholar
[10] Olson, N. (1970) Statistical study of traffic noise. Report APS-476. Div. Physics, Nat. Res. Counc. Canada, Ottawa.Google Scholar
[11] Olson, N. (1972) Survey of motor vehicle noise. J. Acoustical Soc. Amer. 52, 1291–1306.Google Scholar
[12] Rathe, E. J., Casula, F., Hartwig, H. and Mallet, H. (1973) Survey of the exterior noise of some passenger cars. J. Sound and Vibration 29, 483–499.Google Scholar
[13] Tweedie, M. C. K. (1957) Statistical properties of inverse Gaussian distributions, I, II. Ann. Math. Statist. 28, 362–377, 696–705.Google Scholar
[14] Wasan, M. T. (1968) On the inverse Gaussian process. Skand. Aktuarietidskr. 51, 69–96.Google Scholar
[15] Weiss, G. H. (1970) On the noise generated by a stream of vehicles. Transp. Res. 4, 229–233.Google Scholar
[16] Wise, M. E. (1966) Tracer dilution curves in cardiology and the random walk and lognormal distributions. Acta Physiologica Pharmacologic a Neerlandica 14, 175–204.Google Scholar
[17] Takagi, K., Hiramatsu, K., Yamamoto, T. and Hashimoto, K. (1974) Investigations on road traffic noise based on an exponentially distributed vehicles model—single line flow of vehicles with same acoustic power. J. Sound and Vibration 36, 417–431.Google Scholar