ABSTRACT
In the nano-technology era, new probability distributions and new estimators are being identified. There have been several early attempts to estimate parameters using data. The method of maximum likelihood is the most commonly used procedure for estimating parameters. Maximum likelihood estimators (MLE) possess a very useful property known as the invariance property. Although the MLE is a most commonly-used method, it may not be appropriate for every parameter estimation, since it is not necessary that every random sample has a distribution with a known functional form. To compare two estimators using the mean squared error (MSE) is essentially comparing two functions of the parameter. It may happen that one estimator is smaller than the other in the MSE for some portion of the range of the parameter and is larger than the same estimator for the other portion of the range.
