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How can I simulate a data for multiple linear regression (one IV and more then 2 IV) when we know the skewness and kurtosis of the data?

Another question is, how can we determine the type of distribution (ex: gamma dist) based on the skewness and kurtosis? We know that for normal distribution, the skewness and kurtosis are (0,0)...

Thanks

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  • $\begingroup$ Do you mean the skewness and kurtosis of the dependent variable or of the residuals? If it's the former, your problem is complicated by the fact that those moments depend on the regression coefficients themselves and on moments of the IVs. $\endgroup$ – whuber Mar 14 '13 at 3:46
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You'll need to choose some distribution - the first few moments are not enough to pin that down very well.

You might consider assuming the Pearson or the Johnson families of distributions, perhaps.

how can we determine the type of distribution (ex: gamma dist) based on the skewness and kurtosis?

You can't, as explained above, unless you restrict yourself to only considering a family where there's a one-to-one relationship.

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