Statistical methods that do not rely on the assumption of a known population probability distribution function for their validity are called Distribution-free Statistical Methods (also called nonparametric statistical methods). This includes many methods for presenting statistics in graphs, such as histograms, cumulative distribution functions, correlograms, etc. It also includes the calculation of most sample statistics, such as sample means, sample variances, etc. The method is no longer distribution-free when the validity of the method depends on an assumption that specifies the form of the population probability distribution, or specifies that the population distribution comes from a family of population probability distribution functions that are specified except for a finite number of parameters. Then the method is in the class of parametric methods. Usually, the distributional assumption is the assumption that the population has a normal probability distribution, with one or both of the parameters (mean and variance) unspecified. Copyright © 2009 Wiley Periodicals, Inc., A Wiley Company
This article is categorized under:
- Statistical and Graphical Methods of Data Analysis > Bootstrap and Resampling
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These books and papers are good sources of further reading and additional references. Some are early sources of information in topics related to distribution-free methods in statistics, while others are more recent updates.
RELATED WIREs ARTICLE
- 1. Practical Nonparametric Statistics. 3rd ed. New York: John Wiley & Sons; 1999.
- 2 . A Data-Based Approach to Statistics. Belmont, CA: Duxbury Press, Wadsworth Publishing Company; 1994.