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ON CHARACTERIZING DISTRIBUTIONS VIA LINEARITY OF REGRESSION FOR ORDER STATISTICS
Author(s) -
Wesolowski Jacek,
Ahsanullah Mohammad
Publication year - 1997
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1997.tb00524.x
Subject(s) - mathematics , statistics , order statistic , linearity , linear regression , distribution (mathematics) , pareto distribution , order (exchange) , regression analysis , mathematical analysis , physics , finance , quantum mechanics , economics
summary Let X 1 X n be a random sample from an absolutely continuous distribution with the corresponding order statistics X 1:n ≤ X 2:n ≤ X n:n . A complete solution of the problem, posed in 1967 by T. Ferguson, of determining the distribution by linearity of regression of X k+2:n with respect to X k:n is given. The only possible distributions are of the exponential, power and Pareto type. A linear regression relation for exponents of order statistics is also considered.