# Problem with initial guess in Newton-Raphson iteration method

I'm working on estimating the four parameters of Exponentiated Modified Weibull Extension Distribution introduced by Sarhan and Apaloo (2013) with the Maximum Likelihood Estimation (MLE). Because the first derivative of the log-likelihood function of the four parameters give implicit solutions then I tried to continue with the Newton-Raphson iteration method. In any optimization problem, we need some initial guess depend on how much the parameter of distribution. But this thing gives me a little bit problem. I'm not familiar in determining the good initial guess for this method. I have already tried some but nothing give the best solution. My other problem is that I got to exhibit the bathtub shaped hazard curve for the data set I used because my main purpose is to get the good estimated parameters for modelling the bathtub shaped hazard function of the data set. So actually how to choose the good initial guess for this optimization method? Is there any technique in choosing this initial guess?

• In an answer at stats.stackexchange.com/questions/160552, I have claimed that finding good initial values in general "is a bit of an art." I would contend that such a remark is as complete and specific an answer as you could hope for, given the generality of your question. If you would like exhibit the log likelihood function you have in mind and describe the data you have, then perhaps readers would be able to give more specific advice. – whuber Mar 20 '16 at 15:00