Negative Binomial random variable

[sam_0017]

Data is collected on the number of fish caught per day on a month long fishing expedition. It is hypothesised that the data are consistent with a negative Binomial random variable ,X , starting at 0, so that X~Neg Bin(k,p) where E[X]=k(1-p)/p and Var =k(1-p)/p^2 . However, before a hypothesis test can be performed, estimates of k and p (denoted by K`and P`, respectively) are required. Show how you can obtain K` and P` based on the sample mean x` and sample variance s^2 of the fishing data.

 

[Eynstone]

E[X]/Var = p and k=pE[X]/(1-p).