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Biometrika 1971 58(3):631-636; doi:10.1093/biomet/58.3.631
© 1971 by Biometrika Trust
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Distribution of the normal scores estimator of the standard deviation of a normal population

P. PRESCOTT

University of Southampton

The normal scores estimator of the standard deviation of a normal population is an easily obtained unbiased nearly best linear estimator. Its distribution, although difficult to derive explicitly, is shown to be closely approximated by the distribution of cXv/{surd}v, where Xv has a X distribution with v degrees of freedom and c is a scale factor. Exact or approximate values of the parameters c and v are determined which allow the usual tests of significance for the population parameters to be carried out using existing tables of percentage points.

Key Words: Order statistics • Estimate of standard deviation • Quick estimates • Approximation by chi distribution


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