My Math Forum Maximum Likelihood estimation

 April 10th, 2017, 02:32 PM #1 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Maximum Likelihood estimation Trying to find MLE for $\displaystyle \lambda$ of the truncated Poisson distribution tPoisson(λ, k) when k=1 $\displaystyle p_x = \frac{\lambda^x e^{-\lambda}}{q_kx!}$ where: $\displaystyle q_k = 1- \sum_{i=0}^{k} \frac{\lambda^ie^{-\lambda}}{i!}$ $\displaystyle x = k+1, k+2, k+3......$ $\displaystyle \lambda > 0$ $\displaystyle i >= 2$ Log likelihood function: $\displaystyle ln(L(\lambda) = ln [\prod_{}^{\infty}\frac{\lambda^x e^{-\lambda}}{q_kx!} ]$ $\displaystyle ln(L(\lambda) = ln (\lambda) \sum_{}^{\infty} x - n\lambda - nln(q_k) - \sum_{}^{\infty} x!$ when k=1, $\displaystyle q_k = - \lambda e^{-\lambda}$ Normally I would differentiate $\displaystyle ln(L(\lambda)$ with respect to $\displaystyle \lambda$ and equate to 0, to find solution for $\displaystyle \lambda=$, however $\displaystyle ln(q_k)$ results in an error as you cant take natural log of negative numbers, so im not sure how to continue
 April 12th, 2017, 10:37 AM #2 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Please ignore this question, I went wrong further up the question stack, so dont need to do this.

 Tags estimation, likelihood, maximum

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