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I know that Cramer's decomposition theorem says that any normal distribution can be expressed as the sum of multiple normal distributions. I have been searching for a method to divide a data set that constitute a normal distribution to 5 datasets, each of which will be a normal distribution and the sum of which will constitute the 'big' normal distribution I have begun with. Can some of you wizards suggest me a procedure? If you know the SPSS procedure, that will be even sweeter. Thanks a ton, in advance.

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    What are the conditions on your data sets?2012-09-06
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    It's not a sum of normal distributions, but rather a sum of independent random variables that have normal distributions. The operation on distributions, as opposed to that on random variables, is convolution rather than addition. But I think I'd want to know what your data looks like before attempting an answer.2012-09-06
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    PS: I changed the spelling to Cramer, with only one "m". Purists write "Cramér", with an accent.2012-09-06
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    Variance components models, sometimes called random effects models, may be what you're looking for. Google those terms.2012-09-06
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    I should add that Cramer's theorem doesn't say that normal distributions can be decomposed in that way, but rather that they can be decomposed _only_ in that way. I.e. if a normally distirbuted random variable is the sum of independent random variables, then all of the terms in the sum must themselves be normally distributed.2012-09-06
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    Thanks a lot, @MichaelHardy and @Raskolnikov! I have interval data on a 5-point scale. This data has been collected across time. (The data is actually about the type of tourists visiting an attraction and I have data pertaining to this from the time the launch of the attraction took place, when the attraction was growing, when the attraction peaked, when the attraction was declining, and when the attraction was about dead. I want to model the distributions as follows, if possible: http://dl.dropbox.com/u/13145402/diagram%20(1).docx Thanks for your time and effort!2012-09-08

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