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When it comes to representing certain continuous distributions like Gamma or Exponential, some books use the notation (1/theta)×e^(-x/theta), while other books use the notation theta×e^(theta×x) (this is for Exponential dist). Why this difference in notation? Does it make any difference no matter which notation we use? P.S: my teacher said something along the lines of the former notation being correct, because the latter notation poses problems in higher statistics.I didn't quite get it.

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It's a trivial difference. The first is called the scale parameter whereas the latter is rate parameter. The density function is the same. Just the notation changes. For example, you have a density $$ f\left(x\right) = 2e^{-2x}, \quad x>0. $$ Then, you can use either notation $$ \begin{align*} &\operatorname{Exp}\left(2\right)\;\text{(rate)} \\ &\operatorname{Exp}\left(1/2\right) \; \text{(scale)} \end{align*} $$ Once you know which one the author uses, the density will be the anchor that connects both. There's really no importance in which one you should use. You can choose whatever is comfortable.

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  • $\begingroup$ Well, each one has its context where it is more natural! $\endgroup$ Feb 3, 2016 at 16:53
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    $\begingroup$ @kjetilbhalvorsen well yeah, strictly speaking they both have contexts in which one is more appropriate. But they are interchangeable and the difference is really not that big unless you're deriving a density from a differential equation. This is how I think :) $\endgroup$
    – Daeyoung
    Feb 3, 2016 at 16:56

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