1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

MLE of Poisson dist

  1. Nov 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Let [itex] X_1,...,X_n [/itex] be a random sample from a poisson distribution with mean [itex]\lambda[/itex]

    Find the MLE of [itex]\lambda^2 + 1 [/itex]

    2. Relevant equations

    3. The attempt at a solution

    I found [itex]\hat{\lambda}=\bar{x}[/itex]

    Can I just square it and add 1 and solve for lambda hat?

    If not I have no idea how I would get the FOC (with respect to [itex] \lambda^2 + 1 [/itex])

    of the log-likelihood function [itex] \ln{L(\lambda^2+1)}=-n\lambda + \Sigma_{i=1}^n x_i \ln{\lambda} - \ln{\Pi_{i=1}^n x_i!} [/itex]
  2. jcsd
  3. Nov 19, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    That's my understanding of how MLE works. If α is the value of λ that maximises the likelihood of the observed data, then (α2+1) must be the value of λ2+1 that does the same.
  4. Nov 19, 2012 #3
    cool. thanks again.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: MLE of Poisson dist
  1. MLE and related (Replies: 1)