Results 1 to 4 of 4

Math Help - MLE help

  1. #1
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303

    MLE help

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303
    Quote Originally Posted by matheagle View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum