These pages tell about mixture distributions and how to fit them using MIX software.
You get a mixture distribution when you sample from a heterogeneous population. An important example is fisheries length-frequency analysis, where the population is a mixture of distinct age groups. Another application is sampling a mixture of good and defective items for reliability. In psychology, fitting mixture distributions is called "latent class analysis."
Mathematically, the mixed probability density function g is a weighted sum of k component densities.
The components can be normal, lognormal, gamma, exponential, Weibull, binomial, negative binomial or Poisson distributions. The parameters are the mixing proportions and the means and standard deviations of the component distributions.
Read these pages to find out about MIX software and learn how mixture distribution analysis can be used in a variety of applications. You can get a demonstration version of MIX and try some of the examples yourself.
If you have mixture data of your own to analyse, feel free to send me your data and ask me for advice. If you analyse mixture data routinely, you will want to install R on your computer and download and install my R package mixdist.
The original MIX was available commercially from Ichthus Data Systems, for Macintosh, DOS and UNIX. The DOS version ran under Windows (all versions up to and including XP) but only the Macintosh version had a good user interface. This software is no longer supported.
A new version of MIX has been developed as a library package mixdist for the cross-platform open-code R environment. The mixdist package runs on any platform supported by R (UNIX, Linux, Windows, Macintosh). Most of the functionality of MIX has been incorporated in mixdist, with other features to be added soon. The graphics and numerical methods are superior, and mixtures of discrete distributions (binomial, negative binomial and Poisson) are supported in addition to the continuous distributions supported by MIX. Please contact Peter Macdonald for more information. The mixdist package is now a contributed package at CRAN and the current release can be downloaded at no cost. If you have R 2.7.0 or higher installed, you can install mixdist from the Package Installer on the R menu.
Because the Rmix package was completed after Juan Du defended her M.Sc. project, the internal documentation is definitive in cases where it differs from the documentation in her project report.
MIX is developed by Professor Peter Macdonald at McMaster University.
Please send your comments to pdmmac@mcmaster.ca.
MIX software is distributed by:
ICHTHUS DATA SYSTEMS
5235 Trinity Church Road, RR#2
Binbrook, Ontario, Canada L0R 1C0Voice: +1 905 679 9956
Fax: +1 905 522 0935
This article has been translated to Serbo-Croatian language by Jovana Milutinovich from Geeks Education.