Gamma Distribution Confidence Interval

[jaycool1995]

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

 

[SW VandeCarr]

You can get good approximations to the CI of the gamma distribution (which is a two parameter exponential distribution) from the normal, Poisson, or (inverse)chi square approximations. There are also exact methods. This paper discusses all of these methods:

http://wonder.cdc.gov/wonder/help/cancer/FayFeuerConfidenceIntervals.pdf

 

[jaycool1995]

So can i use another distribution to approximate the parameters (e.g the mean) of the gamma dist?
Thanks

 

[SW VandeCarr]

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.

 

[blue_raver22]

for reaching out about this topic! The confidence interval for the parameters of a gamma distribution can be found using a few different methods, depending on the specific parameters and assumptions of the distribution. One common approach is to use the method of moments, where the sample moments (such as the mean and variance) are used to estimate the population moments and then used to calculate the confidence interval. Another method is to use maximum likelihood estimation, where the parameters are estimated by maximizing the likelihood function and then the confidence interval is calculated based on the estimated parameters. There are also other methods such as Bayesian inference and non-parametric approaches that can be used to estimate the confidence interval for gamma distribution parameters. I would recommend consulting with a statistician or using statistical software to determine the best method for your specific data and distribution. Additionally, there are many resources available online and in statistical textbooks that provide step-by-step instructions for calculating confidence intervals for various distributions. I hope this helps and good luck with your research!