Abstract
An algorithm, based on convex quadratic programming, is proposed to smooth sample histograms. The resulting smoothed histogram remains close to the original histogram and honors target mean and variance. The algorithm is extended to smooth sample scattergrams. The resulting smoothed scattergram remains close to the original scattergram shape and the two previously smoothed marginal distributions and honors the target correlation coefficient.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Deutsch, C. V., 1989, DECLUS: A FORTRAN 77 program for determining optimum spatial declustering weights: Computer & Geosciences, v. 15, no. 3, p. 325–332.
Deutsch, C. V., and Journel, A. G., 1992, Geostatistical software library user's guide: Oxford Univ. Press, New York, 340 p.
Gill, P. E., Murray, W., and Wright, M. H., 1981. Practical optimization: Academic Press, New York, 401 p.
Luenberger, D. G., 1984, Linear and nonlinear programming (2nd Ed.): Addison-Wesley, Menlo Park, CA, 491 p.
Scott, D. W., 1992. Multivariate density estimation: theory, practice, and visualization: John Wiley & Sons, New York, 317 p.
Silverman, B. W., 1986, Density estimation for statistics and data analysis: Chapman and Hall, Ltd., New York. 175 p.
Zhu, H., and Journel, A. G., 1992, Formatting and integrating soft data: Stochastic imaging via the Markov-Bayes algorithm,in Soares, A., ed., Geostatistical troia 1992: Kluwer Academic: Publ., Dordrecht, Holland, p. 1–12.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Xu, W., Journel, A.G. Histogram and scattergram smoothing using convex quadratic programming. Math Geol 27, 83–103 (1995). https://doi.org/10.1007/BF02083569
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02083569