MATLAB: Multivariate Linear Regression with Weibull errors

Question

Hi,

I am trying to run a linear regression where the dependent variable lies between 0 and 1. The errors are distributed by 2 parameter Weibull distribution. So essentially I will be estimating 4 parameters: a constant, a parameter for an independent variable and 2 parameters of the weibull distribution. Can somebody guide me as to how I proceed to do this? I am mostly getting search results for survival data but my data is non-survival data. Thanks!

Answer 1

Do some reading about maximum likelihood estimation . This is the general technique one uses for an estimation problem where the errors in the process are assumed to follow some known distribution that is not Gaussian.

Sorry, but I won't write the code for you. One hint I will offer is that it is almost always better to maximize the log (i.e., minimize the negative of the log) of the likelihood function, as otherwise the problem quickly becomes intractable in double precision arithmetic.