<- file stat 97mixture.html -> - also see - 1993 Mixtures-of-gaussians file.

*---------------- (Multimodal) Mixtures

=======================Warren Sarle, 8 Feb 1997==========ssc From: saswss@hotellng.unx.sas.com (Warren Sarle) Subject: Re: Multimodal distributions Message-ID: <E59C2G.2Ho@unx.sas.com> In article <32F64C10.65E6@add.ssw.abbott.com>, Milan Mangeshkar <Milan.Mangeshkar@add.ssw.abbott.com> writes: |> Are there any methods to find whether a distribution has a single peak or |> more than one peak? For mixture distributions, see: Titterington, D.M., Smith, A.F.M., and Makov, U.E. (1985), Statistical Analysis of Finite Mixture Distributions, New York: John Wiley & Sons, Inc. For nonparametric methods, there is no single handy reference: Barnett, V., ed. (1981), _Interpreting Multivariate Data_, New York: John Wiley & Sons, Inc. Girman, C.J. (1994), "Cluster Analysis and Classification Tree Methodology as an Aid to Improve Understanding of Benign Prostatic Hyperplasia," Ph.D. thesis, Chapel Hill, NC: Department of Biostatistics, University of North Carolina. Gitman, I. (1973), ``An Algorithm for Nonsupervised Pattern Classification,'' IEEE Transactions on Systems, Man, and Cybernetics, SMC-3, 66-74. Hartigan, J.A. and Hartigan, P.M. (1985), ``The Dip Test of Unimodality,'' Annals of Statistics_ 13, 70-84. Hartigan, P.M. (1985), "Computation of the Dip Statistic to Test for Unimodality," Applied Statistics, 34, 320-325. Huizinga, D. H. (1978), ``A Natural or Mode Seeking Cluster Analysis Algorithm,'' Technical Report 78-1, Behavioral Research Institute, 2305 Canyon Blvd., Boulder, Colorado 80302. Koontz, W.L.G. and Fukunaga, K. (1972a), ``A Nonparametric Valley-Seeking Technique for Cluster Analysis,'' IEEE Transactions on Computers, C-21, 171-178. Koontz, W.L.G. and Fukunaga, K. (1972b), ``Asymptotic Analysis of a Nonparametric Clustering Technique,'' IEEE Transactions on Computers, C-21, 967-974. Koontz, W.L.G., Narendra, P.M., and Fukunaga, K. (1976), ``A Graph-Theoretic Approach to Nonparametric Cluster Analysis,'' IEEE Transactions on Computers, C-25, 936-944. Minnotte, M.C. (1992), ``A Test of Mode Existence with Applications to Multimodality,'' Ph.D. thesis, Rice University, Department of Statistics. Mizoguchi, R. and Shimura, M. (1980), ``A Nonparametric Algorithm for Detecting Clusters Using Hierarchical Structure,'' IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-2, 292-300. Mueller, D.W. and Sawitzki, G. (1991), ``Excess mass estimates and tests for multimodality,'' JASA 86, 738-746. Polonik, W. (1993), "Measuring Mass Concentrations and Estimating Density Contour Clusters--An Excess Mass Approach," Technical Report, Beitraege zur Statistik Nr. 7, Universitaet Heidelberg. SAS Institute Inc. (1993), SAS/STAT Software: The MODECLUS Procedure, SAS Technical Report P-256, Cary, NC: SAS Institute Inc. Silverman, B.W. (1986), _Density Estimation_, New York: Chapman and Hall. Tukey, P.A. and Tukey, J.W. (1981), ``Data-Driven View Selection; Agglomeration and Sharpening,'' in Barnett (1981). Wong, M.A. and Lane, T. (1983), ``A _k_th Nearest Neighbor Clustering Procedure,'' _Journal of the Royal Statistical Society_, Series B, 45, 362-368. Wong, M.A. and Schaack, C. (1982), ``Using the _k_th Nearest Neighbor Clustering Procedure to Determine the Number of Subpopulations,'' _American Statistical Association 1982 Proceedings of the Statistical Computing Section_, 40-48. -- * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Document by Rich Ulrich. E-mail to wpilib+@pitt.edu

FAQ top.

Ulrich home page.

Ulrich FAQ. http://www.pitt.edu/~wpilib/stats99.html