Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 3, 311-323

A CHARACTERIZATION OF DISTRIBUTIONS BASED ON LINEAR REGRESSION OF ORDER STATISTICS AND RECORD VALUES

By

FERNANDO LO¢ PEZ BLA¢ QUEZ,

And

J. LUIS MORENO REBOLLO, Universidad de Sevilla, Spain

SUMMARY. We obtain the family of distributions for which the regression of one order statistic on another, not necessarily adjacent, is linear. As a consequence, we present a characterization of uniform distributions on an interval. We also characterize the distributions that appear when we impose the condition of linearity of regression for record values.

 AMS (1991) subject classification. 62E10, 62G30.

Key words and phrases. Characterization of distributions, order statistics, record values, linear regression.

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