Skip to main navigation menu Skip to main content Skip to site footer
ACI Avances en Ciencias e Ingenierías

SECTION A: EXACT SCIENCES

Vol. 7 No. 1 (2015)

Empirical Power and Scaling laws of Quito, Guayaquil and other cities in Ecuador

DOI
https://doi.org/10.18272/aci.v7i1.219
Submitted
November 24, 2015
Published
2015-05-22

Abstract

Several papers have shown that distributions characterized by mean and variance are inappropriate for accounting spatial or geographic patterns. The reason is data is not accumulated around a central value; rather, tails become heavy and extreme events result less unlikely than under other distributions. In this sense, this work aims to find empirical laws on some relevant variables of cities in Ecuador, For this purpose, we start from two hypothesis: 1) some socioeconomic variables scales from a size variable, and 2) such variables follow a power law distribution; then estimate needed parameters, and carry out contrasts with adequate heavy tail distributions.

viewed = 675 times

References

  1. Bettencourt 2013. The kind of problem a city is. SFI Working Paper. Santa Fe Institute.
  2. Clauset, A., Shalizi, C. R., and Newman, M. E. 2009. Power-law distributions in empirical data. SIAM review. 51 (4), 661-703.
  3. Batty 2014. Scale, power laws, and rank size in spatial analysis. CASA Working Paper 195. University College London.
  4. Xiao, X., Ethan P., W., Mevin B., H., and Durham, S. L. 2011. On the use of log-transformation vs. nonlinear regression for analyzing biological power laws. Ecology. 92, 18871894.
  5. Vuong, Q. 1989. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica. 57, 307-333.
  6. Fraley, C. and Raftery, A. E. 2002. Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association. 97, 611: 631.
  7. Ma, K., Wang, Z., Jiang, J., Zhu, G., and Li, W. 2011. Power law and small world properties in a comparison of traffic city networks. Chinese Science Bulletin. 56 (34), 3731-3735.
  8. Alstott, J., Bullmore, E., and Plenz, D. 2014. powerlaw: a python package for analysis of heavy-tailed distributions. PloS one. 9 (1), e85777.
  9. Bentley, R. A., Ormerod, P., and Batty, M. 2011. Evolving social influence in large populations. Behavioral ecology and sociobiology. 65 (3), 537-546.
  10. Gillespie, C. S. 2014. Fitting heavy tailed distributions: the poweRlaw package. arXiv preprint arXiv: 1407. 3492.
  11. Newman, M. E. 2005. Power laws, pareto distributions and zipf"™s law. Contemporary physics. 46 (5), 323-351.
  12. Observatorio Metropolitano de Seguridad Ciudadana del Municipio del Distrito Metropolitano de Quito. Delitos contra el patrimonio. Base de datos. 2010-2013.
  13. Shiode, B. M. 2000. Power law distributions in real and virtual worlds. Casa working paper 19. University College London.
  14. Gabaix, X. 2008. Power laws in economics and finance. Technical report. National Bureau of Economic Research.
  15. Instituto Nacional de Estadísticas y Censos (INEC). Censo de Población y Vivienda. Base de datos. 2010.
  16. Instituto Nacional de Estadísticas y Censos (INEC). Geodatabase Empatada Nacional. Información Cartográfica. Versión 2.
  17. Instituto de la Ciudad del Municipio del Distrito Metropolitano de Quito. Matriz de origen destino. Base de datos.
  18. Schlapfer, M., Bettencourt, L., Grauwin, S., Raschke, M., Claxton, R., Smoreda, Z., West, G. B., and Ratti, C. 2012. The scaling of human interactions with city size. arXiv preprint arXiv: 1210. 5215.
  19. Stumpf, M. P. and Porter, M. A. 2012. Critical truths about power laws. Science. 335 (6069), 665-666.