Negative Binomial random variable

In summary, the conversation discusses data collection on the number of fish caught per day on a month-long fishing expedition. The data is assumed to follow a negative Binomial random variable, with parameters k and p, where E[X] represents the expected value and Var represents the variance of the variable. Before conducting a hypothesis test, estimates of k and p, denoted as K` and P`, are needed. These estimates can be obtained using the sample mean x` and sample variance s^2 of the fishing data, where k=pE[X]/(1-p) and p=E[X]/Var.
  • #1
sam_0017
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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.
 
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  • #2


E[X]/Var = p and k=pE[X]/(1-p).
 

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