Gamma Distribution Confidence Interval

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To find the confidence interval for the parameters of the gamma distribution, various methods can be employed, including normal, Poisson, and inverse chi-square approximations, as well as exact methods. A referenced paper provides a comprehensive discussion on these approaches. The gamma distribution's shape varies with the parameter k, which influences the choice of approximation; for k greater than 3, the normal approximation is particularly effective. The value of k can be determined from the probability density function (PDF) of the gamma distribution. Understanding these methods is essential for accurately estimating the confidence intervals for gamma distribution parameters.
jaycool1995
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How would you go about finding the confidence interval for the parameters of the gamma distribution? I have had a look online and haven't found anything with the answer...
Thanks
 
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So can i use another distribution to approximate the parameters (e.g the mean) of the gamma dist?
Thanks
 
jaycool1995 said:
So can i use another distribution to approximate the parameters (e.g the mean) of the gamma dist?
Thanks

Yes. The gamma distribution morphs from Poisson like to normal like "shapes" depending on the parameter k. For k more than 3, the normal approximation is good. "k" relates to the failure or waiting times. k's value can be taken from the PDF where the power of the variable x is k-1.
 
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The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

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