A copula-based approach to accommodate the dependence among microscopic traffic variables

Transportation Research Part C: Emerging Technologies

Volumn 70, Issue , 2016, Pages 53-68

  Zou, Yajie ^a   Zhang, Yunlong ^b  

^a Tongji University   (China)

^b Department of Electrical and Computer Engineering   (United States)

Author keywords

Copula; Headway; Microscopic traffic variables; Multivariate distribution; Speed

Indexed keywords

SPEED;

COPULA; HEADWAY; INDEPENDENT VARIABLES; MARGINAL DISTRIBUTION; MICROSCOPIC TRAFFIC SIMULATION MODELS; MULTIVARIATE DISTRIBUTIONS; TRADITIONAL APPROACHES; TRAFFIC VARIABLES;

DISTRIBUTION FUNCTIONS;

COMPUTER SIMULATION; MULTIVARIATE ANALYSIS; NUMERICAL MODEL; STATISTICAL DISTRIBUTION; TRAFFIC MANAGEMENT; TRANSPORTATION SYSTEM;

AUSTIN; TEXAS; UNITED STATES;

EID: 84949024304     PISSN: 0968090X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trc.2015.11.003     Document Type: Article

References (53)

1. Ali, M.M., Mikhail, N., Haq, M.S., A class of bivariate distributions including the bivariate logistic. J. Multivariate Anal. 8 (1978), 405–412.
2. Bhat, C.R., Eluru, N., A copula-based approach to accommodate residential self-selection effects in travel behavior modeling. Transport. Res. Part B – Methodol. 43 (2009), 749–765.
3. Bhat, C.R., Sener, I.N., A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units. J. Geograph. Syst. 11 (2009), 243–272.
4. Brackstone, M., Waterson, B., McDonald, M., Determinants of following headway in congested traffic. Transport. Res. Part F – Traffic Psychol. Behav. 12 (2009), 131–142.
5. Cherubini, U., Luciano, E., Vecchiato, W., Copula Methods in Finance. 2004, Wiley.com.
6. Clayton, D.G., A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65 (1978), 141–151.
7. Cowan, R.J., Useful headway models. Transport. Res. 9 (1975), 371–375.
8. Demarta, S., McNeil, A.J., The t copula and related copulas. Int. Stat. Rev. 73 (2005), 111–129.
9. Eluru, N., Bhat, C.R., Pendyala, R.M., Konduri, K.C., A joint flexible econometric model system of household residential location and vehicle fleet composition/usage choices. Transportation 37 (2010), 603–626.
10. Embrechts, P., Lindskog, F., McNeil, A., Modelling dependence with copulas and applications to risk management. Handbook Heavy Tailed Distrib. Financ. 8 (2003), 329–384.
11. Embrechts, P., McNeil, A., Straumann, D., Correlation and dependence in risk management: properties and pitfalls. Risk Manage.: Value Risk Beyond, 2002, 176–223.
12. Fisher, N., Switzer, P., Graphical assessment of dependence. Is a picture worth 100 tests?. Am. Stat. 55 (2001), 233–239.
13. Frank, M.J., On the simultaneous associativity of F(x, y) and x + y − F(x, y). Aequat. Math. 19 (1979), 194–226.
14. Genest, C., Favre, A.C., Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrol. Eng. 12 (2007), 347–368.
15. Genest, C., Ghoudi, K., Rivest, L.-P., A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82 (1995), 543–552.
16. Genest, C., Mackay, R.J., Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données. Can. J. Stat. 14 (1986), 145–159.
17. Genest, C., Rivest, L.-P., Statistical inference procedures for bivariate Archimedean copulas. J. Am. Stat. Assoc. 88 (1993), 1034–1043.
18. Gerlough, D.L., Huber, M.J., 1976. Traffic Flow Theory.
19. Grimaldi, S., Serinaldi, F., Asymmetric copula in multivariate flood frequency analysis. Adv. Water Resour. 29 (2006), 1155–1167.
20. Gumbel, E.J., Bivariate exponential distributions. J. Am. Stat. Assoc. 55 (1960), 698–707.
21. Haight, F.A., Mathematical Theories of Traffic Flow. 1963, Academic Press.
22. Haight, F.A., Mosher, W.W., A practical method for improving the accuracy of vehicular speed distribution measurements. Highway Research Board Bulletin 341, 1962, Highway Research Board, Washington, D.C., 92–116.
23. Hofert, M., Mächler, M., McNeil, A.J., Likelihood inference for Archimedean copulas in high dimensions under known margins. J. Multivariate Anal. 110 (2012), 133–150.
24. Hoogendoorn, S.P., Bovy, P.H., New estimation technique for vehicle-type-specific headway distributions. Transport. Res. Rec.: J. Transport. Res. Board 1646 (1998), 18–28.
25. Joe, H., Parametric families of multivariate distributions with given margins. J. Multivariate Anal. 46 (1993), 262–282.
26. Joe, H., Multivariate Models and Dependence Concepts. 1997, CRC Press.
27. Kim, G., Silvapulle, M.J., Silvapulle, P., Comparison of semiparametric and parametric methods for estimating copulas. Comput. Stat. Data Anal. 51 (2007), 2836–2850.
28. Kim, J., Mahmassani, H.S., A finite mixture model of vehicle-to-vehicle and day-to-day variability of traffic network travel times. Transport. Res. Part C: Emerg. Technol. 46 (2014), 83–97.
29. Ko, J., Guensler, R.L., 2005. Characterization of congestion based on speed distribution: a statistical approach using Gaussian mixture model. In: Transportation Research Board Annual Meeting, 2005. Citeseer.
30. Leong, H., 1968. The distribution and trend of free speeds on two lane two way rural highways in New South Wales. In: Australian Road Research Board (ARRB) Conference, 4th, 1968, Melbourne.
31. Luttinen, R., Statistical properties of vehicle time headways. Transport. Res. Rec., 1992, 92–98.
32. Luttinen, R.T., Properties of Cowan's M3 headway distribution. Transport. Res. Rec.: J. Transport. Res. Board 1678 (1999), 189–196.
33. Mclean, J., 1979. Observed speed distributions and rural road traffic operations. In: Australian Road Research Board Conference Proc.
34. Nelsen, R.B., An Introduction to Copulas. 2006, Springer.
35. Park, B.J., Zhang, Y.L., Lord, D., Bayesian mixture modeling approach to account for heterogeneity in speed data. Transport. Res. Part B – Methodol. 44 (2010), 662–673.
36. Ravishankar, K., Mathew, T.V., Vehicle-type dependent car-following model for heterogeneous traffic conditions. J. Transport. Eng. 137 (2011), 775–781.
37. Sarvi, M., Heavy commercial vehicles‐following behavior and interactions with different vehicle classes. J. Adv. Transport. 47:6 (2013), 572–580.
38. Schucany, W.R., Parr, W.C., Boyer, J.E., Correlation structure in Farlie–Gumbel–Morgenstern distributions. Biometrika 65 (1978), 650–653.
39. Schultz, G.G., Rilett, L., Analysis of distribution and calibration of car-following sensitivity parameters in microscopic traffic simulation models. Transport. Res. Rec.: J. Transport. Res. Board 1876 (2004), 41–51.
40. Sklar, M., 1959. Fonctions de répartition à n dimensions et leurs marges, Université Paris 8.
41. Spissu, E., Pinjari, A.R., Pendyala, R.M., Bhat, C.R., A copula-based joint multinomial discrete–continuous model of vehicle type choice and miles of travel. Transportation 36 (2009), 403–422.
42. Taieb-Maimon, M., Shinar, D., Minimum and comfortable driving headways: reality versus perception. Hum. Factors: J. Hum. Factors Ergon. Soc. 43 (2001), 159–172.
43. Tian, Z.Z., Urbanik, T., Engelbrecht, R., Balke, K., Variations in capacity and delay estimates from microscopic traffic simulation models. Transport. Res. Rec.: J. Transport. Res. Board 1802 (2002), 23–31.
44. Wang, M., Hoogendoorn, S.P., Daamen, W., van Arem, B., Happee, R., Game theoretic approach for predictive lane-changing and car-following control. Transport. Res. Part C: Emerg. Technol. 58 (2015), 73–92.
45. Wang, Y., Nihan, N.L., Dynamic estimation of freeway large-truck volumes based on single-loop measurements. Intelligent Transportation Systems, 2004, Taylor & Francis, 133–141.
46. Wasielewski, P., Car-following headways on freeways interpreted by the semi-Poisson headway distribution model. Transport. Sci. 13 (1979), 36–55.
47. Ye, F., Zhang, Y., Vehicle type-specific headway analysis using freeway traffic data. Transport. Res. Rec.: J. Transport. Res. Board 2124 (2009), 222–230.
48. Ye, Z., Zhang, Y., Middleton, D.R., Unscented Kalman filter method for speed estimation using single loop detector data. Transport. Res. Rec.: J. Transport. Res. Board 1968 (2006), 117–125.
49. Yin, S.C., Li, Z.H., Zhang, Y., Yao, D., Su, Y.L., Li, L., 2009. Headway distribution modeling with regard to traffic status. In: 2009 IEEE Intelligent Vehicles Symposium, vols. 1 and 2, pp. 1057–1062.
50. Zhang, L., Singh, V.P., Bivariate flood frequency analysis using the copula method. J. Hydrol. Eng. 11 (2006), 150–164.
51. Zhang, Y., Xie, Y., Ye, Z., 2008. Estimation of large truck volume using single loop detector data. In: Transportation Research Board 87th Annual Meeting.
52. Zou, Y., Zhang, Y., Use of skew-normal and skew-t distributions for mixture modeling of freeway speed data. Transport. Res. Rec.: J. Transport. Res. Board 2260 (2011), 67–75.
53. Zou, Y., Zhang, Y., Zhu, X., Constructing a bivariate distribution for freeway speed and headway data. Transportmet. A: Transport Sci. 10:3 (2014), 255–272.