0
$\begingroup$

I'd like to find a maximum likelihood estimator for $n$ iid exponential random variables. For that I need the joint PDF for those $n$ variables. How can I compute that? In one dimension I would try to work out the cumulative distribution function and then differentiate, but in multiple variables I don't even know where to begin.

$\endgroup$
  • $\begingroup$ Are you looking for a PDF of the sum of these variables? If so, you'll want some sort of gamma distribution $\endgroup$ – Omnomnomnom Dec 28 '16 at 14:25
1
$\begingroup$

In this situation, the variables $X_i$ are independent, therefore the density function of $(X_1,...,X_n)$ is defined as

$$f_{X_1,...,X_n}(x_1,...,x_n)=f_{X_1}(x_1)*...*f_{X_n}(x_n)$$

where $f_{X_i}$ is the density of $X_i$

Because they are identically distributed , we can write :

$$f_{X_1,...,X_n}(x_1,...,x_n)=f_{X_1}(x_1)*...*f_{X_1}(x_n)$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.