Confidence limits on the location parameter of the 3parameter Weibull distribution

[Bharat]

[Originally Posted: 7/10/00--Transferred by ReliaSoft Moderator]

I have been searching articles about obtaining the confidence intervals on the location parameter of the three parameter Weibull distribution. While most of the articles talk about the confidence interval on the shape(beta) and the scale (eta) of the weibull distribution, none talk about the confidence on the location (gamma) parameter. Can some one point to a reference or suggest a method as to how it can be calculated.

Thank you Bharat

[Mike Gumina]

[Originally Posted: 7/30/00--Transferred by ReliaSoft Moderator]

First allow me to appoligize for the crudeness of this message but the website won't allow me to past word equation into this box. If you use the MLE method to find your parameters then finding the confidence interval of the location parameter is not that hard. First you build a sysmetric 3X 3 information matrix using the second partcial derivatives:

row 1 |second partcial of Ln(L) wrt shape, second partcial of Ln(L) wrt shape and scale, second partcial of Ln(L) wrt shape and location|

row2 |second partcial of Ln(L) wrt shape and scale, second partcial of Ln(L) wrt scale, second partcial of Ln(L) wrt shape and location|

row3 |second partcial of Ln(L) wrt location and scale, second partcial of Ln(L) wrt shape and location, second partcial of Ln(L) wrt scale|

you use the cofactor of this matrix/ the determinate of this matrix to get the varience of the location parameter.

Now the confidence interval is t0-K*sqrt(var(t0)) to t0-K*sqrt(var(t0)) where K is the standard normal percential limits. The K value can be found in most advanced statistics texts or maybe the weibull handbook