IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-00372631.html
   My bibliography  Save this paper

Generalizing Ripley's K function to inhomogeneous populations

Author

Listed:
  • Eric Marcon

    (ECOFOG - Ecologie des forêts de Guyane - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - INRA - Institut National de la Recherche Agronomique - UAG - Université des Antilles et de la Guyane - AgroParisTech - CNRS - Centre National de la Recherche Scientifique)

  • Florence Puech

    (LET - Laboratoire d'économie des transports - UL2 - Université Lumière - Lyon 2 - ENTPE - École Nationale des Travaux Publics de l'État - CNRS - Centre National de la Recherche Scientifique)

Abstract

In spatial statistics, Ripley's K function (Ripley, 1977) is a classical tool to analyse spatial point patterns. Yet, it faces two major limits: it is only pertinent for homogeneous point processes and it does not allow the weighting of points.We generalize it to get a new function, M, which oversteps these limits and detects spatial structures of inhomogeneous populations of weighted points.

Suggested Citation

  • Eric Marcon & Florence Puech, 2009. "Generalizing Ripley's K function to inhomogeneous populations," Working Papers halshs-00372631, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00372631
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00372631
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00372631/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. J. O. N. Perkins, 1977. "Comment," Economic Papers, The Economic Society of Australia, vol. 1(56), pages 35-35, October.
    2. J. P. Nieuwenhuysen, 1977. "Comment," Economic Papers, The Economic Society of Australia, vol. 1(53), pages 73-75, January.
    3. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    4. A Getis, 1984. "Interaction Modeling Using Second-Order Analysis," Environment and Planning A, , vol. 16(2), pages 173-183, February.
    5. Jones, Andrew P. & Langford, Ian H. & Bentham, Graham, 1996. "The application of K-function analysis to the geographical distribution of road traffic accident outcomes in Norfolk, England," Social Science & Medicine, Elsevier, vol. 42(6), pages 879-885, March.
    6. Gatrell, A. C. & Bailey, T. C., 1996. "Interactive spatial data analysis in medical geography," Social Science & Medicine, Elsevier, vol. 42(6), pages 843-855, March.
    7. Edward J. Feser & Stuart H. Sweeney, 2000. "A test for the coincident economic and spatial clustering of business enterprises," Journal of Geographical Systems, Springer, vol. 2(4), pages 349-373, December.
    8. S P Kingham & A C Gatrell & B Rowlingson, 1995. "Testing for Clustering of Health Events within a Geographical Information System Framework," Environment and Planning A, , vol. 27(5), pages 809-821, May.
    9. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, June.
    10. J. H. K. Brunner, 1977. "Comment," Economic Papers, The Economic Society of Australia, vol. 1(56), pages 34-35, October.
    11. Eric Marcon & Florence Puech, 2003. "Evaluating the geographic concentration of industries using distance-based methods," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 409-428, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. HAMIDOUCHE M’hamed & BOURCHID ABDELKADER Salim, 2020. "Concentration of Economic Activities in the Kingdom of Saudi Arabia," European Journal of Interdisciplinary Studies, Bucharest Economic Academy, issue 01, March.
    2. Yang Li & Chunyan Xue & Hua Shao & Ge Shi & Nan Jiang, 2018. "Study of the Spatiotemporal Variation Characteristics of Forest Landscape Patterns in Shanghai from 2004 to 2014 Based on Multisource Remote Sensing Data," Sustainability, MDPI, vol. 10(12), pages 1-33, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marcon, Eric & Puech, Florence, 2017. "A typology of distance-based measures of spatial concentration," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 56-67.
    2. Giuseppe Espa & Giuseppe Arbia & Diego Giuliani, 2013. "Conditional versus unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms’ distribution in Milan," Journal of Geographical Systems, Springer, vol. 15(1), pages 31-50, January.
    3. Eric Marcon & Florence Puech, 2012. "A typology of distance-based measures of spatial concentration," Working Papers halshs-00679993, HAL.
    4. Arbia, Giuseppe & Espa, Giuseppe & Giuliani, Diego & Mazzitelli, Andrea, 2010. "Detecting the existence of space-time clustering of firms," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 311-323, September.
    5. Edlin, Aaron S & Reichelstein, Stefan, 1996. "Holdups, Standard Breach Remedies, and Optimal Investment," American Economic Review, American Economic Association, vol. 86(3), pages 478-501, June.
    6. Harvey S. Rosen, 1985. "Housing Behavior and the Experimental Housing-Allowance Program: What Have We Learned?," NBER Chapters, in: Social Experimentation, pages 55-94, National Bureau of Economic Research, Inc.
    7. Pablo Jensen & Julien Michel, 2011. "Measuring spatial dispersion: exact results on the variance of random spatial distributions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 47(1), pages 81-110, August.
    8. Gerald A. Carlino & Jake Carr & Robert M. Hunt & Tony E. Smith, 2010. "The agglomeration of R&D labs," Working Papers 10-33, Federal Reserve Bank of Philadelphia.
    9. Ondřej Šedivý & Antti Penttinen, 2014. "Intensity estimation for inhomogeneous Gibbs point process with covariates-dependent chemical activity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(3), pages 225-249, August.
    10. Eric Marcon & Florence Puech, 2009. "Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods," Working Papers halshs-00372617, HAL.
    11. Kristy Buzard & Gerald A. Carlino & Jake Carr & Robert M. Hunt & Tony E. Smith, 2015. "Localized Knowledge Spillovers: Evidence from the Agglomeration of American R&D Labs and Patent Data," Working Papers 15-3, Federal Reserve Bank of Philadelphia.
    12. Catini, Roberto & Karamshuk, Dmytro & Penner, Orion & Riccaboni, Massimo, 2015. "Identifying geographic clusters: A network analytic approach," Research Policy, Elsevier, vol. 44(9), pages 1749-1762.
    13. Florent Bonneu & Christine Thomas-Agnan, 2015. "Measuring and Testing Spatial Mass Concentration with Micro-geographic Data," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(3), pages 289-316, September.
    14. P. J. Diggle & V. Gómez-Rubio & P. E. Brown & A. G. Chetwynd & S. Gooding, 2007. "Second-Order Analysis of Inhomogeneous Spatial Point Processes Using Case–Control Data," Biometrics, The International Biometric Society, vol. 63(2), pages 550-557, June.
    15. Kristy Buzard & Gerald A. Carlino & Jake Carr & Robert M. Hunt & Tony E. Smith, 2017. "The Agglomeration of American Research and Development Labs," Working Papers 17-18, Federal Reserve Bank of Philadelphia.
    16. Nicoletta D’Angelo & Marianna Siino & Antonino D’Alessandro & Giada Adelfio, 2022. "Local spatial log-Gaussian Cox processes for seismic data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 633-671, December.
    17. Buzard, Kristy & Carlino, Gerald A. & Hunt, Robert M. & Carr, Jake K. & Smith, Tony E., 2017. "The agglomeration of American R&D labs," Journal of Urban Economics, Elsevier, vol. 101(C), pages 14-26.
    18. Edith Gabriel, 2014. "Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 411-431, June.
    19. Jesper Møller & Carlos Díaz‐Avalos, 2010. "Structured Spatio‐Temporal Shot‐Noise Cox Point Process Models, with a View to Modelling Forest Fires," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 2-25, March.
    20. Gabriel Lang & Eric Marcon & Florence Puech, 2020. "Distance-based measures of spatial concentration: introducing a relative density function," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 64(2), pages 243-265, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-00372631. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.