Exploratory Data Analysis
Estimating the Parameters of a Distribution
Non-linear least squares
provides an alternative to maximum likelihood.
The advantages of this method are:
- Non-linear least squares software may be available in many
statistical software packages that do not support maximum
- It can be applied more generally than maximum likelihood.
That is, if your software provides non-linear fitting and
it has the ability to specify the probability function you
are interested in, then you can generate least squares
estimates for that distribution. This will allow you to obtain
reasonable estimates for distributions even if the software
does not provide maximum likelihood estimates.
The disadvantages of this method are:
- It is not readily applicable to censored data.
- It is generally considered to have less desirable optimality
properties than maximum likelihood.
- It can be quite sensitive to the choice of starting values.
Non-linear least squares fitting is available in many general
purpose statistical software programs.