
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Maximum Likelihood Estimators  Actuary  Calculus  0  July 13th, 2015 04:39 AM 
maximumlikelihood estimators  graphist_groupist  Advanced Statistics  1  July 16th, 2012 11:28 PM 
find the maximum likelihood for B  450081592  Advanced Statistics  0  February 21st, 2012 06:30 PM 
maximum likelihood problem  450081592  Advanced Statistics  0  February 21st, 2012 05:50 PM 
Distribution of Maximum Likelihood Estimator  Darkprince  Advanced Statistics  0  October 27th, 2011 12:26 PM 