A Review on Ripley’s K Function in Spatial Analysis

Jaisankar R¹ , Kesavan J²

Section:Review Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.103-107, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.103107

Online published on Apr 30, 2019

Copyright © Jaisankar R, Kesavan J . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Spatial clustering and spatial dependence are the important characteristics of spatial data which are used in methods like disease clustering and spatial dependence in spatial epidemiology. Several procedures like the nearest neighbor method and the quadrat method are developed to contribute these aspects, but the one, called the K- function, developed by Ripley is very significant one on portraying spatial dependence over wide range of scales. This function has salient features both in theory and application. This paper presents a review with reference to the K- function in brief.

Key-Words / Index Term :
Spatial clustering, Spatial dependence, K- Function

References :
[1] Bolibok, L. Limitations of ripley’s K(t) function use in the analysis of spatial patterns on tree stands with heterogeneous structure. ACTA Scientiarum Polonorum 7(1):5-18, 2008.
[2] Cressie, N. A. C. Statistics for spatial data, Wiley, New York, 1991.
[3] Cuzick, J. and Edwards. R. Spatial clustering for inhomogeneous populations (with discussion). Journal of the Royal Statistical Society, Series B 52: 73–104, 1990.
[4] Diggle, P. J. and Chetwynd, A. G. Second-order analysis of spatial clustering for inhomogeneous populations. Biometrics 47(3):1155-1163, 1991.
[5] Diggle, P. J. Statistical analysis of spatial point pattern. 2nd edition, Academic Press, New York, 2003.
[6] Dixon, P. M. Ripley’s K function. John Wiley and Sons 3:1796-1803, 2002.
[7] Gaines, K. F., Bryan, A. L. Jr. and Dixon, P. M. The effects of drought on foraging habitat selection inbreeding wood storks in coastal Georgia. Water birds 23:64–73, 2000.
[8] Gatrell, A. C., Bailey, T. C., Diggle, P. J., Rowlingson, B. S. Spatial Point Pattern Analysis and Its Application in Geographical Epidemiology. Royal Geographical Society with IBG 21(1):256-274, 1996.
[9] Hanisch, K. H. and Stoyan, D. Formulas for second-order analysis of marked point processes, Mathematisc the Operations for schung und Statistic. Series Statistics 14:559–567, 1979.
[10] Isham, V. Multitype Markov point processes: some applications. Proceedings of the Royal Society of London, Series A 391:39–53, 1984.
[11] Li, X., Cao, C and Chang, C. The first law of geography and spatial-temporal proximity. Chinese Journal of Nature 29(2):69-71, 2007.
[12] Lotwick, H. W. and Silverman, B. W. Methods for analyzing spatial processes of several types of points. Journal of the Royal Statistical Society, Series B 44:406–413, 1982.
[13] Neyman, J. and Scott, E. L. A theory of the spatial distribution of galaxies. Astrophysical Journal 116:144–163,1952.
[14] Ripley, B. D. Modeling spatial patterns. Journal of the Royal Statistical Society. Series B (Methodological) 39:172-212, 1977.
[15] Ripley, B. D. The second-order analysis of stationary point processes. Journal of Applied Probability 13(2):255-266, 1976.
[16] Smith, M. O., Ball, J., Holloway, B. B., Erdelyi, F., Szabo, G., Stone, E., Graham, J and Lawrence, J. J. Measuring Aggregation of Events about a Mass Using Spatial Point Pattern Methods. Spat Stat 13:76-89 2015.
[17] Strauss, D. J. A model for clustering. Biometrika 62:467–475, 1975. Zhu, G., Ge, Y and Wang, H. A modified ripley’s K function to detecting spatial pattern of urban system. In International Conference on Geoinformatics, 1-5, Kaifeng, China:IEEE, 2013.