Starting values for MLE

[Peter Shaw]

I want to calculate the MLE of the two-parameter-weibull-distribution. I'm using the nlm function in R which needs starting values. What's the best way of finding reasonable starting values?

P. Shaw

[Dennis Craggs]

While not familiar with the nlm function in R, you can make some initial estimates of the parameters:

(1) Make a guess of the value of beta, the Weibull slope. In many situations an initial estimate of beta = 1 works. If you have any prior knowledge of a better estimate, try it.

(2) Calculate the mean of the data. Then calculate the characteristic life by dividing the mean of the data by the Gamma(1+1/beta) where Gamma is the Gamma function. (Sorry, I can't write a formula here which included the Gamma function or Greek symbols).

If the initial parameter estimates and an optimization function are reasonable, it should converge to an answer. Answers may be different if they optimize different parameters, i.e., minimize error^2, maximize likelihood, ..., etc. of the predicted values vs. the data.

Good luck.

[Peter Shaw]

I have made now a simulation experiment and your solution seems to work: when I'm using your starting values I get the same results as when I'm using the true parameters. Thanks a lot for your help!