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Thread: p-value of negative binomial

  1. #1
    May 2008

    p-value of negative binomial

    Hi, just a quick question, when producing your own data to test if it fits a negative binomial distribution, to find the value of p is it the same procedure as when doing it for a binomial distribution?

    For example in a table

    0 2
    1 1
    2 3 the p-value is (0 X 2)+(1 X 1)+(2 X 3) / (6 X 2)

    = 7/12

    would this be the same for negative binomial???
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  2. #2
    Jul 2008
    Ok, I'm not quite sure what you are doing with your table and I think by the term p-value that you mean the distribution parameter p. Please be more clear about what you are trying to find. p-value has a very specific meaning in statistics. Are you saying that you don't what the population parameter p is, but you ran several experiments and you want to use the results from those experiments to estimate the population parameter p?

    I could be wrong, but based on some googling, it doesn't look like there is 1 accepted way of doing it. Probably the most brain-dead way of doing it would be to average all of the values $\displaystyle \hat{k}$ from your experiments (the number of "failures" in each experiment). Then an estimate of p would be $\displaystyle \frac{r}{\bar{k}+r}$, where $\displaystyle r$ is the number of successes before you terminate the experiment, and $\displaystyle \bar{k}$ is the average of the $\displaystyle \hat{k}$'s.

    This is based on the fact that $\displaystyle \bar{k}$ is an unbiased estimator of the population mean, which is given by $\displaystyle r\frac{1-p}{p}$. Unfortunately, the estimator I gave above is not unbiased. But if the number of experiments you run is sufficiently large then it should be pretty good.

    In fact, this is what wikipedia has listed as a biased estimator (see here)The unbiased estimator does not work for $\displaystyle r=1$. So if your $\displaystyle r>1$ then you can compute the $\displaystyle \hat{p}=\frac{r-1}{r+k-1}$ for each experiment, and then average those.
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