Results 1 to 4 of 4

Math Help - Maximum likelihood

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    4

    Maximum likelihood

    How do I find the mle for r1 and r2 if:

    p(x1,x2) = 1 - r1^x1 * r2^x2 ,

    r1 <1, r2 < 1

    given that x1 and x2 can be either 1 or 0 (i.e. it can be either (0,0), (0,1), (1,1) or (1,0) ?

    Any help will be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    I don't understand this distribution.
    Are you saying that...
    P(X_1=x_1,X_2=x_2)=1-r_1^{x_1}r_2^{x_2}
    then...
    P(X_1=0,X_2=0)=0
    P(X_1=1,X_2=0)=1-r_1
    P(X_1=0,X_2=1)=1-r_2
    and
    P(X_1=1,X_2=1)=1-r_1r_2
    which doesn't sum to one.
    I'm lost.
    Last edited by matheagle; February 24th 2009 at 04:03 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    4
    Here is the full explanation:

    There are two risk factors that may cause an accident to happen. A risk factor x_i is either present (x = 1) or absent (x = 0).

    We have a function that specifies probability p(x1, x2) of an accident, but not the outcome in every concrete case.

    We assume that each risk factor x_i reduces the probability of a good outcome (no accident) by some factor r_i < 1. In other words, the unknown function
    p is of the form p(x_1, x_2) = 1 - r_1^{x_1}  r_2^{x_2}, so we have to learn parameters r_1, r_2.

    How would you compute the ML hypothesis from the data, under the given assumption on p?
    Last edited by Kitano; February 24th 2009 at 01:27 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Once again
    P(X_1=0,X_2=0)=0
    P(X_1=1,X_2=0)=1-r_1
    P(X_1=0,X_2=1)=1-r_2
    and
    P(X_1=1,X_2=1)=1-r_1r_2
    doesn't sum to one.
    Something is off here.
    I can differentiate and estimate the two r's, but that seems to be meaningless here.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maximum likelihood
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: December 20th 2011, 02:17 AM
  2. maximum likelihood
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 19th 2011, 12:53 PM
  3. Maximum Likelihood
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 10th 2011, 02:14 PM
  4. Maximum Likelihood.
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 15th 2009, 08:54 AM
  5. Maximum Likelihood
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 20th 2009, 06:45 AM

Search Tags


/mathhelpforum @mathhelpforum