Weibull distribution and correlation coefficient

[Tushar Radke]

[Originally Posted: 1/20/00-- Transferred by ReliaSoft Moderator]

I have a question for anyone who would bother to help me out. Abernethy has plot out a graph showing a certain minimum value for correlation coefficient depending on the distribution and the sample size. i.e. to say that he claims that R-squared value of 0.95 could be acceptable for Two parameter Weibull distribution but not so for three parameter distribution given sample size of say 20. Can anyone of you please justify this to me? Thanks a lot for your time. Please mail me at Tushar_Radke@hotmail.com

[Crawford Smith]

[Originally Posted: 2/4/00-- Transferred by ReliaSoft Moderator]

Abernethy's "Critical Correlation Coefficients" are guidelines that were generated via simulation, not rigorous statistic derivation. As such, they should not be used as the sole judgement as to whether or not a particular distribution is an appropriate fit to a dataset. Considering that the reason these "critical coefficients" were generated in the first place was to deal with "small" datasets, I don't think that one should have any trouble determining the appropriate distribution to model a dataset with 20 failures. At any rate, there are many other measures of goodness of fit beyond the correlation coefficient and its "critical" values. Each data set and analysis should be judged on its own merits, so to speak, and not necessarily on simulation-generated measures.