Choosing the good initial value of the Newton-Raphson iteration method for Maximum Likelihood Estimation

I want to estimate the four parameters of Exponentiated Modified Weibull Extension (EMWE) distribution introduced by Sarhan and Apaloo (2013) with the Maximum Likelihood Estimation. 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. It's just that I am not familiar in determining the good initial value for this method. Does anyone know how to determine the good initial value for the Newton-Raphson iteration method? Are there any special requirements in determining this value?

Answer 1

[Matt J]

There is no systematic choice of an initial guess in any optimization problem. In Max Likelihood problems, though, a common choice is to choose initial parameters that match the empirical moments (mean, variance, etc...) of the observed data.

[Christian Beren]

This distribution has four parameters consisting of two scale parameters and also two shape parameters. So actually, what value that scale parameter and shape parameter could describe for?