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1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.6. Probability Distributions Estimating the Parameters of a Distribution

Least Squares

Least Squares Non-linear least squares provides an alternative to maximum likelihood.
Advantages The advantages of this method are:
  • Non-linear least squares software may be available in many statistical software packages that do not support maximum likelihood estimates.

  • 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.
Disadvantages 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.
Software Non-linear least squares fitting is available in many general purpose statistical software programs.
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