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Linear Estimation of Parameters of the Cauchy Distribution Based on Sample Quantiles

Gwenda J. Cane
Journal of the American Statistical Association
Vol. 69, No. 345 (Mar., 1974), pp. 243-245
DOI: 10.2307/2285535
Stable URL: http://www.jstor.org/stable/2285535
Page Count: 3
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Linear Estimation of Parameters of the Cauchy Distribution Based on Sample Quantiles
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Abstract

Asymptotically best linear unbiased estimates (ABLUE) of the location and scale parameters (when both are unknown) of the Cauchy distribution, based on k order statistics selected from a large sample, are considered. It is shown that the joint asymptotic relative efficiency (JARE) of the two estimates is maximized when the sample quantiles are equally spaced, and expressions are derived for the coefficients used in these estimates. In estimating the scale parameter using a reasonably large number of quantiles, it is found that not much weight is attached to the extreme observations or those close to the median.

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