A random sample of n data values is obtained from a process having an absolutely continuous cdf of unknown shape.

A random sample of n data values is obtained from a process having an absolutely continuous cdf of unknown shape. The metallurgist wants to select the best fitting distribution among several candidate cdfs. She decides to select the distribution which has mean and variance most closely matching the corresponding sample mean and variance. The major weakness in this approach is

1. the mean and variance may be highly inflated by outliers
2. there are many distribution having the same mean and variance but very different shapes
3.  she should have used robust estimators of the location and scale parameters
4. the empirical distribution function contains more information about the tails of the distribution than does the mean and variance
5. the moments of a distribution determine the distribution, hence there is no weakness in the approach