Geografie 2009, 114, 282-297
https://doi.org/10.37040/geografie2009114040282
Nomothetic geography revisited: statistical distributions, their underlying principles, and inequality measures
References
1. , L. A. N., OTTINO, J. M. (2004): Complex networks: Augmenting the framework for the study of complex systems. The European Physical Journal B, 38, No. 2, pp. 174–162.
<https://doi.org/10.1140/epjb/e2004-00110-5>
2. , C., FRENKEN, K., HELLERVIK, A. (2006): A complex network approach to urban growth. Environment and Planning A, 38, No. 10, pp. 1941–1964.
<https://doi.org/10.1068/a37418>
3. AITCHINSON, J., BROWN, J. A. C. (1957): The Lognormal Distribution. Cambridge University Press, Cambridge, 176 p.
4. , F. (1913): Das gesetz der bevolkerungskoncentration. Petermanns Geographische Mitteilungen, 59, No. 1, pp. 74–76.
5. , A., YOUNG, M., GLEDITSCH, K. S. (2007): On the frequency of severe terrorist events. Journal of Conflict Resolution, 51, No. 1, pp. 58–87.
<https://doi.org/10.1177/0022002706296157>
6. COLE, J. P., KING, C. A. M. (1968): Quantitative geography: techniques and theories. Wiley, London, 692 p.
7. , F. A., FLACHAIRE, E. (2007): Income distribution and inequality measurement: The problem of extreme values. Journal of Econometrics, 141, No. 2, pp. 1044–1072.
<https://doi.org/10.1016/j.jeconom.2007.01.001>
8. , D. R., WEINSTEIN, D. W. (2002): Bones, bombs, and break points: the geography of economic activity. American Economic Review, 92, No. 5, pp. 1269–1289.
<https://doi.org/10.1257/000282802762024502>
9. , P., HAMPL, M. (1995): Geographical organization and societal development: searching for an integral approach. Acta Universitatis Carolinae Geographica, XXX, No. 1–2, pp. 21–42.
10. , J. A., PRAIRIE, Y. T., COLE, J. J., DUARTE, C. M., TRANVIK, L. J., STRIEGL, R. G., MCDOWELL, W. H., KORTELAINEN, P., CARACO, N. F., MELACK, J. M., MIDDELBURG, J. (2006): The global abundance and size distribution of lakes, ponds, and impoundments. Limnology and Oceanography, 51, No. 5., pp. 2388–2397.
<https://doi.org/10.4319/lo.2006.51.5.2388>
11. , M. (1941): Sur la loi de répartition de certaines grandeurs géographiques. Journal de la Societé de Statistique de Paris, 82, 114–122.
12. , X. (1999): Zipf’s law for cities: an explanation. Quarterly Journal of Economics, 114, No. 3, pp. 739–767.
<https://doi.org/10.1162/003355399556133>
13. GABAIX, X., IOANNIDES, Y.M. (2003): The evolution of city size distributions. In: Henderson, J. V., Thisse, J. F. (ed.): Handbook of urban and regional economics, IV: Cities and geography, North-Holland, Amsterdam, pp. 2341–2378.
14. GALTON, F. (1869): Hereditary Genius: an Inquiry into its Laws and Consequences. London, Macmillan, 390 p.
15. , F. (1879): The geometric mean, in vital and social statistics. Proceedings of the Royal Society 29, pp. 365–367.
16. GIBRAT, R. (1931): Les inégalités économiques. Librarie du Recueil Sirey, Paris.
17. , P. D. (2000): Arithmetic or geometric normality of biological variation: an empirical test of theory. Journal of Theoretical Biology, 204, No. 2, pp. 201–221.
<https://doi.org/10.1006/jtbi.2000.2008>
18. , R, MOSSA, S, TURTSCHI, A., AMARAL, L. A. N. (2005): The worldwide air transportation network: anomalous centrality, community structure, and cities’ global roles. PNAS, 102, No. 22, pp. 7794–7799.
<https://doi.org/10.1073/pnas.0407994102>
19. , B., RICHTER, R. F. (1944): Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, No. 4, pp. 185–188.
20. , S. (1998): A theoretical framework for abundance distributions in complex systems. Complexity International, 6, No. 12, pp. 1–12.
21. HAMPL, M. (2000): Reality, society and geographical/environmental organization: searching for an integrated order. Charles University. Prague, 112 p.
22. HAMPL, M. (1998): Realita, společnost a geografická organizace: hledání integrálního řádu. Přírodovědecká fakulta UK, Praha, 110 p.
23. HAMPL, M. (1971): Teorie komplexity a diferenciace světa. Praha, Univerzita Karlova, 183 p.
24. JONASSON, K. (2008): Documentation for life expectancy at birth (years) for countries and territories. Gapminder Documentation 004, Stockholm, www.gapminder.com.
25. , T. (2003): Scaling behavior in land markets. Physica A: Statistical Mechanics and its Applications, 326, No. 1–2, pp. 256–264.
<https://doi.org/10.1016/S0378-4371(03)00145-6>
26. , J. (1941): Přírodní dualita statistického rozložení. Statistický obzor, 22, pp. 171–222.
27. , J. (1938): Deux types fondamentaux de distribution statistique. Prague, Comité d’organisation, Bull. de l’Institute Int’l de Statistique, vol. 3, pp. 295–299.
28. , V. (1928): Zpráva o zeměpisně-statistickém atlasu. Věstník Československé akademie věd a umění, pp. 61–67.
29. , M., SOLOMON, S. (1996): Power laws are logarithmic Boltzmann laws. International Journal of Modern Physics C, 7, No. 4, pp. 595–601.
<https://doi.org/10.1142/S0129183196000491>
30. , W., CAI, X. (2004): Statistical analysis of airport network of China. Physical Review E, 69, No. 4, pp. 1–6.
31. , E., STAHEL, W. A., ABBT, M. (2001): Log-normal distributions across the sciences: keys and clues. Bioscience, 51, No. 5, pp. 341–352.
<https://doi.org/10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2>
32. , B., MOREIN, G., TURCOTTE, D. (1998): Forest fires: an example of self-organized critical behavior. Science, 281, No. 5384, pp. 1840–1842.
<https://doi.org/10.1126/science.281.5384.1840>
33. , B. B. (1975a): Earth’s relief, shape and fractal dimension of coastlines, and number area for islands. PNAS, 72, No. 10, pp. 3825–3838.
<https://doi.org/10.1073/pnas.72.10.3825>
34. MANDELBROT, B.B. (1975b): Les Objets Fractals, Forme, Hasard et Dimension. Flammarion, Paris, 190 p.
35. , M. (2003): A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1, No. 2, pp. 226–251.
<https://doi.org/10.1080/15427951.2004.10129088>
36. , K., PACZUSKI, M. (1995): Emergent traffic jams. Physical Review E, 51, No. 4, pp. 2909–2918.
<https://doi.org/10.1103/PhysRevE.51.2909>
37. , P., NOSEK, V. (2009): Přístupy k měření významu geografického rozměru společenských nerovnoměrností. Geografie, 114, No. 1, pp. 52–65.
38. , M. E. J. (2005): Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46, No. 5, pp. 323–351.
<https://doi.org/10.1080/00107510500052444>
39. , J. (2006): Negativní vlivy společensko-ekonomických nerovností a mechanismy jejich regulace. Ekonomický časopis, 54, No. 7, pp. 709–724.
40. , J. (2007): On the measurement of regional inequality: does spatial dimension of income inequality matter? Annals of Regional Science, 41, No. 3, pp. 563–580.
<https://doi.org/10.1007/s00168-007-0113-y>
41. , D. (2004): Complexity science and human geography. Transactions of the Institute of British Geographers, 29, No. 3, pp. 282–295.
<https://doi.org/10.1111/j.0020-2754.2004.00321.x>
42. , F. W. (1948): The commonness and rarity of species. Ecology, 29, No. 3, pp. 611–627.
43. QUETELET, A. (1835): Sur l’homme et le développement de ses facultés, ou essai de physique sociale. Livre second. Bachelier, Paris, 327 p.
44. , L. F. (1948): Variation of the frequency of fatal quarrels with magnitude. Journal of the American Statistical Association, 43, No. 244, pp. 523–546.
<https://doi.org/10.1080/01621459.1948.10483278>
45. , D., TURCOTTE, D. (1998): Fractality and self-organized criticality of wars. Fractals, 6, No. 4, pp. 351–357.
<https://doi.org/10.1142/S0218348X98000407>
46. SILVERMAN, B. W. (1986): Density Estimation for Statistics and Data Analysis. Chapman and Hall, London, 212 p.
47. , H. A. (1955): On a class of skew distribution functions. Biometrika, 42, No. 3/4, pp. 425–440.
<https://doi.org/10.1093/biomet/42.3-4.425>
48. , H. A., BONINI, CH. (1958): The size distribution of business firms. The American Economic Review, 48, No. 4, pp. 607–617.
49. , A. L., ŠTORCH, D., ŠIZLINGOVÁ, E., REIF, J., GASTON, K. J. (2009): Speciesabundance distribution results from a spatial analogy of central limit theorem. PNAS, 106, No. 16, pp. 6691–6695.
<https://doi.org/10.1073/pnas.0810096106>
50. THOMAS, R. W., HUGGETT, R. J. (1980): Modelling in geography: a mathematical approach. Barnes and Noble, New Jersey, 338 p.
51. , W. (1970): A computer movie simulating urban growth in the Detroit region. Economic Geography, 46, No. 2, 234–240.
<https://doi.org/10.2307/143141>
52. , D. (1995): Scaling in geology: landforms and earthquakes. PNAS, 92, No. 15, pp. 6697–6704.
<https://doi.org/10.1073/pnas.92.15.6697>
53. , A., HAZARI, B. R. (2004): Zipf’s law strikes again: the case of tourism. Journal of Economic Geography, 4, No 4, pp. 459–472.
<https://doi.org/10.1093/jnlecg/lbh030>
54. , J. C., YULE, G. U. (1922): Some statistics of evolution and geographical distribution in plants and animals, and their significance. Nature, 109, pp. 177–179.
<https://doi.org/10.1038/109177a0>
55. ZIPF, G. K. (1949): Human behaviour and the principle of least effort. Addison-Wesley, Reading MA.
