Methodology and Computing in Applied Probability

, Volume 14, Issue 3, pp 785–791 | Cite as

Goodness-of-Fit and Sufficiency: Exact and Approximate Tests



A procedure to test fit to a distribution where a minimal sufficient statistic is available, is discussed for testing the Poisson distribution. The test is exact, and is compared with a simpler approximate test. A remarkable correlation between the p-values given by the exact and the approximate procedures is found, and shows the power of the computer over and above what is usually acknowledged.


Cramér-von Mises tests Empirical distribution function Lehmann’s test Poisson distribution 

AMS 2000 Subject Classifications

62B05 62G10 62E17 


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  1. Lehmann EL, Romano JP (2005) Testing statistical hypotheses, 3rd edn. Springer, New YorkMATHGoogle Scholar
  2. Lockhart RA (2011) Conditional limit laws for goodness-of-fit tests. Bernoulli (forthcoming)Google Scholar
  3. Lockhart RA, O’Reilly FJ, Stephens MA (2007) Use of the Gibbs sampler to obtain conditional tests, with applications. Biometrika 94:992–998MathSciNetMATHCrossRefGoogle Scholar
  4. Lockhart RA, O’Reilly FJ, Stephens MA (2009) Exact conditional tests and approximate bootstrap tests for the von Mises distribution. J Stat Theory Pract 3:543–554MathSciNetMATHCrossRefGoogle Scholar
  5. O’Reilly F, Gracia-Medrano L (2006) On the conditional distribution of goodness-of-fit tests. Commun Stat, Theory Methods 35:541–549MathSciNetMATHCrossRefGoogle Scholar
  6. Stephens MA (1986) Tests based on EDF statistics. In: D’Agostino RB, Stephens MA (eds) Chapter 4 in goodness-of-fit techniques. Marcel Dekker, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Statistics and Actuarial ScienceSimon Fraser UniversityBurnabyCanada

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