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Convenient Probability Plotting Positions for the Normal Distribution

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  • V. Barnett

Abstract

It is known that highly efficient unbiased estimators of the mean, μ, and standard deviation, σ, of a normal distribution can be obtained by probability plotting methods (Chernoff and Lieberman, 1954; Barnett, 1975). These estimators are the sample mean, and the best linear unbiased order statistics estimator (BLUE), for and a, respectively. They arise from plotting positions Φ(b/b′b) where Φ is the standard normal distribution function and b the vector of coefficients in the BLUE of a. Alternative linear unbiased order statistics estimators of μ and σ proposed by Gupta (1952) are much simpler in form and fully efficient for μ whilst the efficiency loss for σ is a mere 0.1 per cent. It turns out that the Gupta estimators can also be obtained by probability plotting methods for an appropriate choice of plotting positions. These plotting positions are far more convenient to use than Φ(b/b′b) and would appear to be the sensible choice if we require simultaneously a clear indication of the validity of the normal model and unbiased estimators of (almost) full efficiency.

Suggested Citation

  • V. Barnett, 1976. "Convenient Probability Plotting Positions for the Normal Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(1), pages 47-50, March.
    • Handle: RePEc:bla:jorssc:v:25:y:1976:i:1:p:47-50
    DOI: 10.2307/2346518
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