Difference between the terms ‘joint distribution’ and ‘multivariate distribution’?

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

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