Solving Nonlinear Equations in Weibull

[Park, sang jun]

[Originally Posted: 11/12/99-- Transferred by ReliaSoft Moderator]

Hello I am Ph.D. candidate in KAIST. I am wonder what algorithm do you use to obtain MLE of Weibull or Lognormal distribution. I tried many algorithm such as Newton-Raphson, Powell, etc, but I can't obtain good soluton.. Would you tell me which algorithm do you used?? Sincerely yours.. Park, sang-jun

[David J. Groebel]

[Originally Posted: 11/12/99-- Transferred by ReliaSoft Moderator]

In Weibull++, the first partial derivatives of the Log-Likelihood Function are solved simultaneously to get the estimates of the parameters. When using MLE, the graphical initial estimates might have been shifted if the data set contains many suspensions. In addition, for some parameter combinations the MLE solution will break down and fail to exist. Maximum Likelihood estimates are badly behaved in the vicinity of Beta = 1.

[dean.m.ford@delphiauto.com]

[Originally Posted: 11/12/99-- Transferred by ReliaSoft Moderator]

If you are starting with an Excel spreadsheet, then just use the "solve for" option. It almost always works if you use a reasonable starting value. If you really want to code your own, the "downhill simplex method" as described in the "Numerical Recipes" books by Press, Flannery, Teukolsky, and Vetterling work well at finding the maximum of the log likelihood. Good luck!

[Park]

[Originally Posted: 11/12/99-- Transferred by ReliaSoft Moderator]

Thanks for your kindness advice..