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I would like to know if my two-dimensional data set to follow any of the following distributions such as the mixed multivariate normal model, multivariate t model, multivariate non-central t model. Are there well-known tests to know if I may apply them to my data set?

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    $\begingroup$ You can simulate data to follow any given distribution and then use ks.test to check if your data matches any of your simulated distributions. $\endgroup$ – Alex Firsov Mar 27 '17 at 14:43
  • $\begingroup$ @Alex thank you very much, if so how may I simulate these distributions using what input values? they depend on the estimated values. Then the question would be how to estimate these input values based on the observed dataset? $\endgroup$ – rsc05 Mar 27 '17 at 15:27
  • $\begingroup$ The distributions you're interested in can be simulated with the mvtnorm package. If you'd like to work with others, check out this question for simulating custom distributions. $\endgroup$ – Alex Firsov Mar 28 '17 at 0:54
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    $\begingroup$ What for do you want to conduct such tests? $\endgroup$ – Tim Jul 11 '18 at 8:41
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A good answer would require knowing some context. The answer given in comments above is not entirely correct. To simulate from one of this distributions, you would have to first estimate parameters, using your data. But the KS test is only correct when the null hypothesis distribution is entirely prespecified, so using it (uncorrected) after parameter estimation is incorrect.

One possibility would be to estimate all of the distributions in your (short!) list by maximum likelihood, and compare them by information criteria like the AIC.

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    $\begingroup$ Beyond the excellent points here: The OP would need a two-dimensional analogue of the KS test in any case. $\endgroup$ – Nick Cox Jul 11 '18 at 8:47

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