Negative binomail distribution and its variance

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SUMMARY

The discussion centers on estimating the variance of the negative binomial distribution using maximum likelihood estimation (MLE) and Fisher's information. The original poster struggles with deriving the variance despite understanding its theoretical basis. A suggestion is made to reformulate the problem into the exponential family form to facilitate the derivation. Additionally, the accuracy of the log-likelihood function is questioned, indicating potential errors in the MLE calculation.

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  • Understanding of negative binomial distribution properties
  • Familiarity with maximum likelihood estimation (MLE)
  • Knowledge of Fisher's information and its application
  • Basic concepts of the exponential family of distributions
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  • Study Fisher's information and its role in statistical inference
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Statisticians, data scientists, and researchers involved in statistical modeling and estimation techniques, particularly those working with the negative binomial distribution.

_joey
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Hi,

I am trying to estimate variance for negative Binomial distribution using
maximum likelihood estimation and Expected (Fisher's) information to determine its variance. I know what variance is for this distrubution but I cannot derive it.


Here is my solution. Any comments and suggestions are much appreciated

Thanks!

Solution: http://img825.imageshack.us/img825/7545/ndist.png
 
Last edited by a moderator:
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I think I know what the problem is. I've been solving problems for many hours and I need a break. :)
 
Have you tried putting it into the form of the exponential family first?

Your MLE = x bar is incorrect. What did you get for your log-likelihood function?
 

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