Small-Sample Tests for the Equality of Two Normal Cumulative Probabilities, Coefficients of Variation, and Sharpe Ratios

  • A. J. HayterEmail author
  • Jongphil Kim


This article considers the problem of testing the equality of the cumulative probabilities of two independent normal distributions. This is equivalent to the problem of testing the equality of the coefficients of variations from two separate populations, which in turn is equivalent to the problem of testing the equality of two Sharpe ratios in financial analyses when it is assumed that the data are normally distributed. This is a problem that has received considerable attention in the statistical and financial research literature; although, while previous approaches have relied upon large sample asymptotic results, the objective of this article is to develop a test procedure that guarantees the nominal confidence level for small sample sizes. Examples are provided to demonstrate the new test procedure, and software is available for its implementation from the authors.


Cumulative distribution function Coefficient of variation Sharpe ratio Normal distribution Two-sample comparison Noncentral t-distribution Test procedure Acceptance set 

AMS Subject Classification



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© Grace Scientific Publishing 2015

Authors and Affiliations

  1. 1.Department of Business Information and AnalyticsUniversity of DenverDenverUSA
  2. 2.Department of BiostatisticsH. Lee Moffitt Cancer Center & Research InstituteTampaUSA

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