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enter image description here

For a multivariate data set, I test normality on the marginals, and I get plots like above.

That's not my actual plot.... mine is not that obvious, the middle part is actually quite straight.... but the sharp decline/rise near the ends is the same as in my plots.

So, what does this tell us. Which model, if not the multivariate normal, should I use?

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    $\begingroup$ 1. Marginal normality doesn't indicate multivariate normality. You can have the first and yet be nowhere near having the second. 2. interpretation of QQ plots is covered by many questions on site - two are indicated above but searching will help you find others. 3. Your diagram actually looks like a quantile plot (effectively inverse-ecdf) rather than a quantile-quantile plot but the image is so poor it's impossible to clearly read what is plotted (the only named axis is unreadable) $\endgroup$
    – Glen_b
    Commented Mar 23, 2017 at 1:17

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