Koksma–Hlawka Inequality

Fred J. Hickernell

Research output: Chapter in book/report/conference proceedingEntry for encyclopedia/dictionarypeer-review


The Koksma–Hlawka inequality is a tight error bound on the approximation of an integral by the sample average of integrand values. The integration error is bounded by a product of two terms, the discrepancy of the sample points, [equation image], and the variation of the integrand, V(g). These two quantities measure the quality of the sample points and the roughness of the integrand, respectively. The Koksma–Hlawka inequality plays a key role in the development of quasi–Monte Carlo methods. Such methods replace simple random sample points by low discrepancy points. The Koksma–Hlawka inequality has also influenced the study of experimental design and led to the creation of UNIFORM DESIGNS.

Original languageEnglish
Title of host publicationEncyclopedia of Statistical Sciences
EditorsSamuel Kotz, Campbell B. Read, N. Balakrishnan, Brani Vidakovic, Norman L. Johnson
Number of pages5
ISBN (Electronic)9780471667193
Publication statusPublished - 15 Jul 2004
Externally publishedYes


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