Advertisement

Likelihood ratio tests for comparingk populations —The two-parameter nonregular models

  • Shaul K. Bar-lev
  • Benzion Boukai
Article

Summary

The null and nonnull distributions of the likelihood ratio statistics for testing the homogeneity ofk given populations, each associated with a nonregular density depending on two truncation parameters, are investigated. This generalizes to the two-parameter case the work of Hogg (1956,Ann. Math. Statist.,27, 529–532), Barr (1966,J. Amer. Statist. Assoc.,61, 856–864) and Khatri and Jaiswal (1969,Aust. J. Statist.,11, 79–84; 1969, 1971,Ann. Inst. Statist. Math.,21, 127–136;23, 199–210).

Key words

Nonregular distributions likelihood ratio tests power functions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Andersen, E. B. (1971). The asymptotic distribution of conditional likelihood ratio tests,J. Amer. Statist. Assoc.,66, 630–633.CrossRefGoogle Scholar
  2. [2]
    Barr, D. R. (1966). On testing the equality of uniform and related distributions,J. Amer. Statist. Assoc.,61, 856–864.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Basu, D. (1955). On statistics independent of a complete sufficient statistic,Sankhya,15, 377–380.MathSciNetzbMATHGoogle Scholar
  4. [4]
    Gradshtein, I. S. and Ryzhik, I. M. (1965).Tables of Integrals, Series, and Products (4th ed.), Academic Press, New York.Google Scholar
  5. [5]
    Hogg, R. V. (1956). On the distribution of the likelihood ratio,Ann. Math. Statist.,27, 529–532.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Khatri, C. G. and Jaiswal, M. C. (1969). Testing the equality of distributions when the range depends upon the parameter,Aust. J. Statist.,11, 79–84.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Jaiswal, M. C. and Khatri, C. G. (1969). The power function of the likelihood ratio test when range depends upon the parameter,Ann. Inst. Statist. Math.,21, 127–136.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Jaiswal, M. C. and Khatri, C. G. (1971). On certain tests and monotonicity of their power for the parameters involved in the nonregular density functions,Ann. Inst. Statist. Math.,23, 199–210.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1986

Authors and Affiliations

  • Shaul K. Bar-lev
    • 1
  • Benzion Boukai
    • 1
  1. 1.University of HaifaIsrael

Personalised recommendations