Modelling is based on assumptions. Maximum likelihood estimation is based on the assumption of independence, normality and homoscedasticity of observations. If normality is not fulfilled, but with independence and homoscedasticity, the least square procedure may be applied. The method of moments may be applied if the probability distribution underlying the data is known.

Thank you Ette Etuk for your kind and prompt response.

Professor Etuk descriptions are very good and complete. There are some other estimation techniques which are useful in applications which may also be useful to you such as

Quasi-Likelihood estimator

Weighted least-square estimator

Minimum spacing distance estimator

L-Moments Estimators

Method of percentile estimation (Estimators Based on Percentiles)

Method of maximum product of spacing

The Cramer-von Mises maximum goodness-of-fit estimators

The Anderson-Darling maximum goodness-of-fit estimators

Thanks Seyed Mahdi Amir Jahanshahi for your contributions.

I think the maximum entropy method has been missed out of the above lists (It is not the same as the maximum likelihood method).

Thank you for your contributions Malcolm White.