1. MLE help

Suppose that $\displaystyle Y_{1},...Y_{n}$ constitute a random sample from the density function

$\displaystyle f(y|\theta)=e^{-(y-\theta)}$ for $\displaystyle y>\theta$ and zero elsewhere, where $\displaystyle \theta$ is an unknown, positive constant.

Q: Find an estimator for $\displaystyle \hat{\theta}$ for $\displaystyle \theta$ by the method of maximum likelihood.

A: Consider the likelyhood function $\displaystyle L(\theta)=\Pi_{i=1}^{n}e^{-(y-\theta)}=e^{n\theta\\-\sum_{i=1}^{n}y_{i}}$.
Then,
$\displaystyle ln[L(\theta)]=ln[e^{n\theta\\-\sum_{i=1}^{n}y_{i}}]=n\theta-\sum_{i=1}^{n}y_{i}$.
Thus, the partial derivative with respect to $\displaystyle \theta$ equals $\displaystyle n$.

So, I am doing something wrong, because this attmept is a dead end.

2. this was just posted and solved

1 no need to take the log
2 you need the indicator function
3 calc will not work, you need comment sense, to maximize wrt THETA.
But go search for this problem in the threads here.

3. Originally Posted by matheagle
this was just posted and solved