Confidence intervals

[Bharat]

[Originally Posted: 12/1/00--Transferred by ReliaSoft Moderator]

I have been searching articles about obtaining the confidence intervals on the location parameter of the three parameter Weibull distribution. Can some one point to a reference or suggest a method as to how it can be calculated.

Thank you Bharat

[Dr. Dave Olwell]

[Originally Posted: 12/1/00--Transferred by ReliaSoft Moderator]

Confidence intervals for the location parameter in the 3P Weibull are problematic. The MLE estimates do not mee tthe conditions for the assumption of asymptotic normality. Rank regression confidence bounds also have technical problems. Meeker/Escobar (page p. 622-623) discuss this issue and provide some references.

These difficulties are the reason that Weibull++ recommends that you estimate the threshold parameter using rank regression, and then coniditon on it to do the MLE analysis for the other two parameters, and why we do not report confidence bounds for threshold parameters in general.

You can illustrate the problem yourlef by fitting a two parameter exponential model to a data set, and looking at the 3d likelihood plot. You won't be able to find a maximum,

Best wishes,

Dr. Dave