Distribution of Likelihood Criteria and Box Approximation

  • A. K. Gupta
  • J. Tang
Part of the Theory and Decision Library book series (TDLB, volume 8)


In this paper, the exact distribution of a random variable whose moments are a certain function of gamma functions (Box, 1949), has been derived. It is shown that Box’s asymptotic expansion can be obtained from this exact distribution by collecting terms of the same order. From the point of view of computation, the derived series has a distinct advantage over the results of Box since the coefficients satisfy a recurrence relation.

Key words and phrases

Asymptotic Distribution Percentage Points Convergence Recursive Formula Test of Independence 


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Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1987

Authors and Affiliations

  • A. K. Gupta
    • 1
  • J. Tang
    • 2
  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenJapan
  2. 2.Bell Communications ResearchPiscatawayUSA

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