Talk:Mixture distribution

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I have only seen these two terms used synonomously 205.155.65.236 06:30, 31 October 2007 (UTC)

Rename[edit]

Should we rename this to Mixture distribution so as to include the discrete case? —3mta3 (talk) 12:27, 24 June 2009 (UTC)

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I suggest to rename this to Mixture family, similarly to how we have the exponential family. Unlike all other “distribution” articles, this model cannot be completely described by a finite number of parameters, there always remains freedom in choosing the “mixed-in” densities pi(x), just like there is a similar freedom in the exponential family.  … stpasha »  15:20, 16 January 2010 (UTC)

Simulation[edit]

I think the text should include a Simulation chapter. It's very easy to simulate a variable: first, sample from the discrete set {1, 2, ... n} with weights wi and get i, then simulate the i-th distribution. Is there any source for this? Albmont (talk) 17:29, 1 July 2009 (UTC)

Incorrect diagram[edit]

An IP editor plavedthis in the main text "-this is wrong it shows the concept, but the "mixed normal pdf" should be underneath the 3 pdf's because each pdf integrates to 1 on its own." I have hidden both this and the diagram for now. Melcombe (talk) 15:55, 28 June 2010 (UTC)

Incorrect formula for variance (2nd momentum; Section 'Moments')[edit]

There appears to be a mistake in the formula for the variance of a mixture distribution: The general formula is:

For j=2 (Variance), we get:

This is different to the formula from the article:

I believe the mistake is that

Edits[edit]

I altered the statement that the variance formula applied to normal distributions only. It is general.

Source: https://statisticalmodeling.wordpress.com/2011/06/16/the-variance-of-a-mixture/ — Preceding unsigned comment added by Svein Olav Nyberg (talkcontribs) 22:25, 17 November 2015 (UTC)

Finite, countable, uncountable mixtures[edit]

The term discrete is more concise than "finite and countable". Also, the term continuous feels better than uncountable here even though it's more restrictive. More accessible to someone with just a calculus background. Then we could make note that it generalizes in the context of measure theory. — Preceding unsigned comment added by 207.11.1.161 (talk) 08:44, 20 February 2016 (UTC)

Generating functions[edit]

There should be a new section about moment generating (and maybe characteristic) functions of mixture distributions. Kjetil B Halvorsen 15:10, 19 April 2017 (UTC) — Preceding unsigned comment added by Kjetil1001 (talkcontribs)