Kajian Eksistensi Distribusi Hukum Pangkat Pada Kota-Kota di Indonesia

Hoferdy Zawani, Pradono Pradono


The  notion  of  Power-law  which arguably  stands  for  the  sign of  complex  system  has  been  widely  encountered  in  many  natural  and  social phenomenons  as  upon which  we  hypothesize  Indonesian  cities’  size distribution  would  follow  the  same  manner.  To  evaluate  it,  we  test  the hypothesis  employing  hybrid  method  co-joined  the  Cumulative Distribution  Function  (CDF)  technique,  Hill  Estimator,  and  Anderson Darling  Statistics  (Coronel-Brizio,  dkk,  2003;  Coronel-Brizio  and Hernandez-Montoya, 2004) on Indonesian cities’ population at year 1990 and  2005.  As  results,  in  one  hand,  our  work  brings  quantitative  sight upon Indonesian cities distribution within which were satisfied by  Powerlaw  distribution  for  both  year  1990  (Xmin=9665  and Alpha=2,088±0,094)  and  year  2005  (Xmin=129490  and Alpha=1,994±0,078)  while  in  the  other  hand, it  strengthens  the  precede Power-law  Indonesian  cities  distribution  claim  which  previously proposed  by  Mulianta, dkk (2004).  Put the  result altogether  and  have it tested with deductive and simulation method as we try to explain on how the distribution could ever happen have lead us to conceive the notion of ‘onslaught’  urbanization  in Indonesia. All and all,  the work solidifies the edge  of  chaos  paradigm  in  Indonesian  urban  and  regional  planning study.


statistic; extreme value theory; simulation; and urban distribution

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Alexander, Ernest R. (1992). Approaches to Planning. Gordon and Breach Science Publishers

Alfarano, Simone Dipl. Phys. (2006), An Agent-Based Stochastic Volatility Model, Disertasi Doktors der Wirtshaft- und Sozialwissenshaftlichen Fakult¨at der Cristian-Albrechts-Universit¨at zu Kiel, Kiel: Germany

Batty, Michael dan Torrens, Paul M., 2001, Modeling Complexity: the Limits to Prediction, Center for Advance Spatial Analysis, University of College London, United Kingdom, www.casa.ucl.ac.uk

Batty, Michael and Cole, Sam. (1997). Time And Space: Geographic perspectives on the future. Futures, Vol. 29, No. 415: 217-289

Batty, M., dkk. 2006. "Visualization in Spatial Modelling". dalam Complex Artificial Environment. J. Portugali, ed. Springer-Verlag Berlin Heidelberg.

Batty, M. dan Torrens,Paul M. (2005). Modelling and prediction in a complex world. Futures 37 (2005) 745–766

Barnsley, Michael (1993) Fractals Everywhere, Second Edition, AP Professional.

Bertalanffy, L. von (1969) General System Theory. New York: Brazilier.

Buldyrev, S.V., dkk. (2003) “Hierarchy in Social Organization”. Physica A 330 (2003): 653 – 659

Castillo, Enrique dan Ali S. Hadi (1997) “Fitting the Generalized Pareto Distribution to Data”, Journal of the American Statistical Association, Vol. 92, No. 440: 1609-1620

Chen, Kan dan Bak, Per. (2002) “Forest Fires and the Structure of the Universe”. Physica A 306 (2002): 15 – 24

Churchman, C. W. (1968), The Systems Approach, Dell Publishing Company, New York.

Coronel-Brizio, H. F., de la Cruz-Laso, C. R., dan Hernandez-Montoya, A. R. (2003) “Fitting the Power-law Distribution to the Mexican Stock Market Index Data”, Facultad de F´ısica e Inteligencia Artificial. Universidad Veracruzana, Apdo. Xalapa, Veracruz: Me´xico. Sumber internet: http://arXiv:cond-mat/0303568 v1 27 Mar 2003, diakses bulan desember 2004.

Coronel-Brizio, H. F. dan Hernandez-Montoya, A. R., (2004) “On Fitting the Pareto-Levy Distribution to Stock Market Index Data: Selecting a Suitable Cutoff Value”, Facultad de F´ısica e Inteligencia Artificial. Universidad Veracruzana, Apdo. Xalapa, Veracruz: M´exico. Sumber internet: http://arXiv:cond-mat/0411161 v1 6 Nov 2004, diakses bulan desember 2004

Craib, Ian (1992), Modern Social Theory: From Parsons to Habermas, 2nd edition, Harvester Wheatsheaf.

Darley, Vince. (1994), Emergent Phenomena and Complexity, in R. Brooks & P. Maes, eds, `Artificial Life IV, Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems', The MIT Press. Sumber internet dari http://www.santafe.edu/~vince/

Dempster, M. Beth L., A Self-Organizing Systems Perspective on Planning for Sustainability, 1998, Tesis Master of Environmental Studies on Planning, University of Waterloo, Ontario: Canada.

Friedmann, John (1987) Planning in the Public Domain: From Knowledge to Action . Princeton University Press

Goldstein, Michel L., dkk. 2004. “Problems with Fitting to the Power-Law Distribution”. School of Electrical and Computer Engineering, Oklahoma State University. Sumber internet: http:// arXiv:cond-mat/0402322 v3 13 Aug 2004, diakses bulan Desember 2005

Gopalakrishnan, G. (2002), Computation Engineering: Applied Automata Theory and Logic, draft version, State University of New York, Stony Brook.

Herbert, W. (1994), Algorithms and Complexity, internet edition, University of Pennsylvania, Philadelphia.

Hogg, Robert dan Craig, Allen. Introduction to Mathematical Statistics, 1995, Prentice Hall, New Jersey: USA. Hordijk, W. (1994) Dynamics Emergent Computation and Evolution in Cellular Automata, Erasmus University Rotterdam, Rotterdam

Kant, Immanuel. (1781) Critique of Pure Reason. Diterjemahkan oleh Kingsmill Abbott, Thomas. (1952). Longsmans, Green & Co., New York and London. Dibawah Hak Cipta Internasional milik Encyclopædia Britannica, Inc.

Kuhn, Thomas S. (1970) The Structure of Scientific Revolutions, International Encyclopaedia of Unified Science Volume II Number 2, the University of Chicago Press: USA

Langton, C. G. (1990) “Computation at the Edge of Chaos: Phase Transitions and Emergent Computation”. Physica D, 42, 12-27.

Mantegna, Rosario N., dan Stanley, H. Eugene, (2000) An Introduction to Econophysics-Correlations and Complexity in Finance, Cambridge University Press: UK

Mitchell, Melanie (1998) Computation in Cellular Automata: A Selected Review, in "Nonstandard Computation", edited by T. Gramss, S. Bornholdt, M. Gross, M. Mitchell, and T. Pellizzari, VCH Verlagsgesellschaft.

Moura Jr., Newton J. dan Ribeiro, Marcelo B. (2006) “Zipf Law for Brazilian Cities”. Physica A 367 441-448

Mulianta, Ivan., Situngkir, Hokky., dan Surya, Yohanes (2004) “Power Law Signature in Indonesian Population”, WPT04. Bandung Fe Institute

Newman, M. E. J., “Power laws, Pareto distributions and Zipf‟s law”, 2006, Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor: USA. Sumber internet dari: http://arXiv:cond-mat/0412004 v3 29 May 2006, diakses bulan april 2006

Newman, M,E.J. (1997). “Evidence for Self-Organized Criticality in Evolution”. Physica D 107 (1997) 293-296

Otter, H.S., A. Veen, dan HJ. de Vriend (2001) ABLOoM: Location behaviour, spatial patterns, and agent-based modelling, Journal of Artificial Societies and Social Simulation vol. 4, no. 4.

Papon, P., J. Leblond and P.H.E. Meijer (2006). The Physics of Phase Transitions Concepts and Applications, Springer-Verlag.

Popper, K. R. (1959) The Logic of Scientific Discovery, Hutchinson, London. Portugali, Jouval, “The Scope of Complex Artificial Environments”, 2006 dalam Portugali, Jouval (ed.), Complex Artificial Environments- Simulation, Cognition, and VR in the Study and Planning of Cities, 2006, Springer-Verlag Berlin, Heidelberg: Germany

Reed, William J., dan Hughes, Barry D. (2003). “On the Distribution of Family Names”. Physica A 319 579 – 590

Rittel, Horst W. J., dan Webber, Melvin M., “Dilemmas in a General Theory of Planning”, 1973, Policy Sciences (4):155-169, Elsevier Scientific Publishing Company, Amsterdam

Schuster, Heinz Georg. 1995. Deterministic Chaos: An Introduction, third augmented edition. VCH Verlagsgesselshaft mbH. Federal Republic of Germany.

Situngkir, Hokky (2003-...) “Tutorial Sosiologi Komputasional”. Dept. Comp. Soc. Bandung Fe Institute. Sumber internet: http://www.bandungfe.net, diakses bulan Desember 2005

Sinha, Sitabhra. (2006). “Evidence for Power-law Tail of the Wealth Distribution in India”. Physica A 359 555–562

Situngkir dan Khanafiah, 2007. “Bird‟s Eye View to Indonesian Mass Conflict”. WPG07. Bandung Fe Institute.

Stanley, Eugene. 1971. Introduction to Phase Transitions and Critical Phenomena. Oxford University Press.

Stephens, M.A., "EDF Statistics for Goodness of Fit and Some Comparisons", 1974, Journal of the American Statistical Association 69: 730-737

Turcotte, D. dan B. Malamud (2004). “Landslides, Forest Fires, and Earthquakes: Examples of Self-organized Critical Behavior”, Physica A 340 (2004) 580 – 589

Wachs, M. (1995). Foreword in Planning Ethics: A Reader in Planning Theory, Practice and Education, S. Hendler, ed., Center for Urban Policy Research

Weinberg, Gerald M., (2001) An Introduction to General System Thinking, Dorset House Publishing Co. Inc., New York: USA

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