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  • 1.  Mixtures of Distributions

    Posted 07-22-2012 18:07
    This message has been cross posted to the following eGroups: Statistical Computing Section and Statistical Consulting Section .
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    My apologises for cross posting.
    Dear all,
    Good day!

    Is anybody there who is professional on the issue of "Mixtures of Distributions"? I have some questions about the formulations of mixtures of distributions and programing them in a software like R.
    What I'd like to know are :
    -          Formulation of two Gaussian Distributions
    -           Formulations of three Gaussian Distributions and even more than 3 dist.
    -          Formulations of two Poisson Distributions or even more.
    -          Formulations of Logistic and two Poisson Distributions
    -          Formulations of a Gaussian and a Logistic
    Any help in form of introducing webpages, books, booklets or papers will be appreciated.
    Thank you all for your attention.

    All the best,
    Amir

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    Amir Kasaeian
    PhD Student in Biostatistics
    Tehran University of Medical Sciences (TUMS)
    amir_kasaeian@yahoo.com
    akasaeian@razi.tums.ac.ir
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  • 2.  RE:Mixtures of Distributions

    Posted 07-22-2012 20:22
    Amir, In 1984, when i was studying statistics at Iowa Stae, I took my second theory course for my master's degree from Noel Cressie. I remembered his being interested in mixtures of normal distributions. A quick search on Google gives two papers he and another wrote on the subject at the time. Margot Tollefson ------------------------------------------- Margot Tollefson Owner Vanward Statistical Consulting -------------------------------------------
    Original Message


  • 3.  RE:Mixtures of Distributions

    Posted 07-22-2012 22:51
    There is a discussion of using mixtures of distributions and carrying out the computations using proc NLIN and NLMIXED.

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    George Milliken
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    Original Message


  • 4.  RE:Mixtures of Distributions

    Posted 07-23-2012 09:08
    Mclust does model based clustering which is in effect fitting mixtures of normal distributions.  For other clustering (i.e., fitting mixtures) you can try flexmix.

    I hope this helps,
    Robert

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    Robert Podolsky
    Georgia Health Sciences University
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  • 5.  RE:Mixtures of Distributions

    Posted 07-23-2012 11:14
    Most responses are pointing you to software. I will mention methodology.  These models can all be approach using maximum likelihood with a constraint on the proportions summing to 1.  The method of solution is usually via the EM algorithm.  If you need to choose the order (number of distributions to include) variable selection methods such as AIC and BIC could be used.  I provide a bootstrap solution in to the selection problem in Section 8.3 of my book "Bootstrap Methods".  Here are some amazon links to my book and the mixture books:
    http://www.amazon.com/Mixture-Models-Statistics-Textbooks-Monographs/dp/0824776917/ref=sr_1_1?s=books&ie=UTF8&qid=1343052425&sr=1-1&keywords=McLachlan+and+Basford

    http://www.amazon.com/Finite-Mixture-Models-Probability-Statistics/dp/0471006262/ref=sr_1_1?ie=UTF8&qid=1343056380&sr=8-1&keywords=mixture+models

    http://www.amazon.com/Bootstrap-Methods-Practitioners-Researchers-Probability/dp/0471756210/ref=sr_1_2?s=books&ie=UTF8&qid=1343056428&sr=1-2&keywords=bootstrap+methods
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    Michael Chernick
    Director of Biostatistical Services
    Lankenau Institute for Medical Research
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    Original Message


  • 6.  RE:Mixtures of Distributions

    Posted 07-23-2012 12:50
    Sorry I was not more complete in my response.  In addition to the texts mentioned, the "manuals" for both mclust and flexmix provide some good information about mixture models and fitting in R.  The link for the Mclust manual is http://www.stat.washington.edu/research/reports/2012/tr597.pdf.  Flexmix has 2 papers that describe the R package and the types of models that can be fit: http://www.jstatsoft.org/v11/i08/paper/ and http://www.jstatsoft.org/v28/i04/paper/. 

    I hope these papers help also,
    Robert

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    Robert Podolsky
    Georgia Health Sciences University
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    Original Message