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Linearity of regression for adjacent order statistics-discrete case

Dembińska A.

Demonstratio Mathematica

2001

Vol. 34, nr 3

711-721

Let X1X2 be a random sample from a discrete distribution on the integers with the corresponding order statistics X1:2 m) = ajXj:2+bj where m is a nonnegative integer, a, b -some constants and i,j należy {1,2}, i = j. However some of the main results of that paper are not complete or incorrect. In this note, developing Nagaraja's ideas, the family of distributions with the linearity of regression property is completely characterized.