Results 1 to 9 of 9

Math Help - maximum likelihood estimators help

  1. #1
    Newbie
    Joined
    Aug 2011
    Posts
    7

    maximum likelihood estimators help

    X1, X2, .... ,Xn are independet exponential random variables with E(Xk)=k times lambda where k = 1,2,...,n. What is the sufficient statistics and maximum likelihood estimators of lambda??? and is it unbiased?

    (a) sufficient statistics i got summation of Xk where k is from 1 to n

    (b) MLE i got (1/n) times summation (Xk)/k where k is from 1 to n

    (c) it is unbiased

    Is my answers all correct??please reply me..thank you!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6

    Re: maximum likelihood estimators help

    Hello,

    The sufficient statistics would rather be \sum kX_k. You can't isolate \sum X_k itself.

    Please do the caculations again, the MLE is something like \frac{n}{\sum kX_k}

    And it will indeed be unbiased since the expectation of the texponential distribution is 1/(k*lambda)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2011
    Posts
    7

    Re: maximum likelihood estimators help

    why the MLE is n/sigma(k*Xk) ??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2011
    Posts
    7

    Re: maximum likelihood estimators help

    isnt the sufficient stat is summation (Xk)/k ??
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6

    Re: maximum likelihood estimators help

    Awww yes, I was using the pdf \lambda e^{-\lambda x}, but it seems like you're using the \frac 1\lambda e^{-x/\lambda} one...

    For the MLE it is then correct. So your answers are correct.


    As a sidenote, it would have been much better if you had shown your working...
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Aug 2011
    Posts
    7

    Re: maximum likelihood estimators help

    yea, thank you. i have my working but it is in handwriting, a bit difficult to type here. i will scan it later.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Aug 2011
    Posts
    7

    Re: maximum likelihood estimators help

    I have another problem. Let X1,X2,...,Xn be a random sample of size n from a distribution with density function f(x;theta) = c2^[-(x-theta)^2]. if theta is known, the MLE of c is infinity is it?? i formed the likelihood function and take the derivative of the ln of the function then let it equal to zero.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6

    Re: maximum likelihood estimators help

    Are you sure you have to consider the MLE of c ??? Because c is just a constant to make the function a pdf (integral equal to 1)
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Aug 2011
    Posts
    7

    Re: maximum likelihood estimators help

    oh..but the question is like that..i think i just stick to my answer which is infinity. And i wanna ask if i want to find the 95% confidence interval of theta, after i found the estimator of theta, how to find the distribution of it?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maximum Likelihood
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 10th 2011, 02:14 PM
  2. Maximum likelihodd estimators
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: April 12th 2010, 07:03 AM
  3. Maximum Likelihood Estimators
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 7th 2009, 01:48 PM
  4. Maximum Likelihood Estimators
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 2nd 2009, 05:22 AM
  5. Maximum Likelihood.
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 15th 2009, 08:54 AM

Search Tags


/mathhelpforum @mathhelpforum