MLE help

**Danneedshelp** · March 24th, 2010, 03:30 PM

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

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

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

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

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

**matheagle** · March 24th, 2010, 03:37 PM

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.

**Danneedshelp** · March 24th, 2010, 03:40 PM

Originally Posted by matheagle

this was just posted and solved

My bad. I am sorry about that.

Before I look in the other thread, I think I found the solution. Looking the function, wouldn't the max value be given by the minimum order statistic? I think I figured it out using the indicator function.

Sorry again, I will look through the threads before posting next time.

**matheagle** · March 24th, 2010, 03:47 PM

here's the same problem
http://www.mathhelpforum.com/math-he...34065-mle.html

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