Abstract: It is indicated in this paper that errors of extreme distributional parameters by maximum likelihood method are obviously different due to different samplings. The difference of the errors is increasing with decresasing of sample sizes. The "beautiful sampling method" by which estimated errors are likely zero, and "the most probable samlping method" which samples are veridical are debeloped. The difference of the errors of the both sampling methods indicates it is required to improve the maximum likelihood method to improve the estimation precision as small sample sizes.

Key words: sampling, likelihood estimation