Gamma and Weibull location parameter estimation

[monicamlmc]

Hi all,

I have a set of samples and I would like to detect the probability distribution that best represents the data. I'm using the kolmogorov-Smirnov test to verify the goodness-of-fit for some well-known distributions, like Gamma, exponential and Weibull. Since I don't know the distribution parameters, I'm estimating them (using the mechanism of rank regression on Y in most cases).

My problem is that I need to extend my set of tested distributions adding the three-parameter weibull and three-parameter gamma distributions. However, I can't find a "direct" method to estimate the location parameter for both distributions. By "direct" I mean some closed formula. I found some iterative methods, but I'm trying to avoid them because speed of detection is a very important factor in my work. Btw, I'm a Computer Science student, I have a very limited background in statistics... :-( may be what I want to do is not possible, I don't know...

Can anyone help me?

Thanks in advance!

 

[marcusl]

Matlab's Statistical toolkit has estimators for these distributions. I've used the Weibull one, can't remember if it does all three parameters. You input the raw data and it gives you parameter fits.

 

[tacman]

Hello,

Thank you for sharing your question and background information. Estimating the location parameter for the three-parameter Weibull and Gamma distributions can be done using the method of moments or maximum likelihood estimation. However, these methods do involve some iterative calculations, so they may not be the most efficient for your purposes.

Another approach you can consider is using the method of moments with the rank regression estimator you mentioned. This involves using the sample mean and variance to estimate the shape and scale parameters, and then using the rank regression estimator to estimate the location parameter. This method may be more efficient for your needs as it does not involve iterative calculations.

I hope this helps and good luck with your analysis!