The frequency distribution for the m-th largest of n observations

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1959

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Abstract

Two divergent lines of investigation were persued. (a) The work by B. Gnedenko on the asymptotic limiting forms for the frequency distribution of the largest of a set of observations was translated into English, reviewed, and extended to include the asymptotic forms for the m-th largest.of n observations (m finite). (b) The work by Wilks, Cramer, Gumbel, and others on the exact frequency distribution for the m-th largest of n obersvations was generalized to permit a discontinuous population distribution. Extensive tables were prepared to facilitate calculations with the exact distribution and a number of illustrative examples computed. The numerical methods used in preparing the tables are outlined in the Appendix. The unifying role of the parameter wn(x), wn(x) = n [ l-F(x)] where F(x) is the population; frequency distribution was emphasized throughout both lines of investigation.

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