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Most Stringent Test for Location Parameter of a Random Number from Cauchy Density

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Listed:
  • Atiq-ur-Rehman, Atiq-ur-Rehman
  • Zaman, Asad

Abstract

We study the test for location parameter of a random number from Cauchy density, focusing on point optimal tests. We develop analytical technique to compute critical values and power curve of a point optimal test. We study the power properties of various point optimal tests. The problem turned out to be different in its nature, in that, the critical value of a test determines the power properties of test. We found that if for given size α and any point θm in alternative space, if the critical value of a point optimal test is 1, the test optimal for that point is the most stringent test.

Suggested Citation

  • Atiq-ur-Rehman, Atiq-ur-Rehman & Zaman, Asad, 2008. "Most Stringent Test for Location Parameter of a Random Number from Cauchy Density," MPRA Paper 13492, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:13492
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    File URL: https://mpra.ub.uni-muenchen.de/13492/1/MPRA_paper_13492.pdf
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    References listed on IDEAS

    as
    1. Nora Gürtler & Norbert Henze, 2000. "Goodness-of-Fit Tests for the Cauchy Distribution Based on the Empirical Characteristic Function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 267-286, June.
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    Cited by:

    1. Maxwell L. King & Sivagowry Sriananthakumar, 2015. "Point Optimal Testing: A Survey of the Post 1987 Literature," Monash Econometrics and Business Statistics Working Papers 5/15, Monash University, Department of Econometrics and Business Statistics.

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    • A23 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Graduate

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