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Intervals and tests for weighted sum of percentiles θ(p) and θ(1−p) for symmetrical populations

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Abstract

Available is a random sample from a distribution that is continuous, symmetrical, and reasonably well-behaved. Approximate one-sided and two-sided confidence intervals (provide tests) are developed forAθ(p)+Bθ(1−p), where θ(p) is the population 100p percentile, 1/2≦p<1, andA, B can be any positive or negative numbers. The interquantile and other ranges are special cases. Asymptotically, a confidence coefficient value is precisely determined. The statistics used are weighted sums (with weightsA andB) of two percentage points of the sample. Many comparisons of population percentiles can be made through suitable choice ofp, A, andB.

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Reference

  1. Walsh, John E. (1957). Nonparametric mean estimation of percentage points and density function values,Ann. Inst. Statist. Math.,8, 167–180.

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Authors and Affiliations

  1. University of Texas at Arlington, Arlington, USA

    Grace J. Kelleher & John E. Walsh

Authors
  1. Grace J. Kelleher
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  2. John E. Walsh
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Also consultant to the Defense Communications Agency, Washington, D.C.

John E. Walsh died 24 August 1972. Research partially supported by Department of Labor Grant 31-46-70-06 and by Mobil Research and Development Corporation. Also associated with ONR Contract N00014-68-A-0515 and NASA Grant NGR 44-007-028. Performed at American University.

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Kelleher, G.J., Walsh, J.E. Intervals and tests for weighted sum of percentiles θ(p) and θ(1−p) for symmetrical populations. Ann Inst Stat Math 27, 525–527 (1975). https://doi.org/10.1007/BF02504670

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  • DOI: https://doi.org/10.1007/BF02504670

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