I am writing about using a ‘joint probability distribution’ for an audience that would be more likely to understand ‘multivariate distribution’ so I am considering using the later. However, I do not want to loose meaning while doing this.

Wikipedia seems to indicate that these are synonyms.

Are they? If not, why not?

**Answer**

The terms are basically synonyms, but the usages are slightly different. Think about the univariate case: you may talk about “distributions” in general, you might more specifically refer to “univariate distributions”, and you refer to “the distribution of $X$”. You *don’t* normally say “the univariate distribution of $X$”.

Similarly, in the multivariate case you may talk about “distributions” in general, you might more specifically refer to “multivariate distribution”, and you refer to “the distribution of $(X,Y)$” or “the joint distribution of $X$ and $Y$”. Thus the joint distribution of $X$ and $Y$ *is* a multivariate distribution, but you *don’t* normally say “the multivariate distribution of $(X,Y)$” or “the multivariate distribution of $X$ and $Y$”.

**Attribution***Source : Link , Question Author : David LeBauer , Answer Author : Mark Meckes*