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Maximum likelihood error

  1. Oct 29, 2008 #1
    1. The problem statement, all variables and given/known data

    pdf: f(x)=ax^(a-1) ; 0<x<1, a>0
    estimate a by maximum likelihood

    2. Relevant equations
    let L be maximum likelihood
    L=(a(x[1])^(a-1))(a(x[2])^(a-1))...(a(x[n])^(a-1))

    3. The attempt at a solution

    Im trying to make this into a nicer expression:
    L=a^n... (now im stuck)

    Any help would be v much appreciated.
    Thank you.
     
  2. jcsd
  3. Oct 29, 2008 #2

    statdad

    User Avatar
    Homework Helper

    Remember that if your density is [tex] f(x) [/tex], then the likelihood function for an i.i.d. sample is

    [tex]
    L(x_1, \dots, x_n) = \prod_{i=1}^n f(x_i)
    [/tex]

    For the density you give this is

    [tex]
    L(x_1, \dots, x_n) = \prod_{i=1}^n a x_i^{a-1} = a^n \prod_{i=1}^n x_i^{a-1}
    [/tex]

    What do you know about simplifying a product of different bases when each is raised to the same power?
     
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