A characterization of the rectangular distribution

Eugene Lukacs

Stochastic Processes and their Applications, 1979, vol. 9, issue 3, 273-279

Abstract: It is assumed that the statistics S and T (given by formula (1.2) and (1.3)) have constant regression on [Lambda]= [summation operator]nj=1 Xj. Under cetain additonal assumptions this leads either to a symmetric two point distribution or the rectangular distribution over (-1, +1). The two point distribution can be excluded by assuming that the population distribution function is continuous. A characterization theorem for the rectangular distribution over (-1, +1), is then obtained.

Keywords: Rectangular; (uniform); distribution; characteristic; function; symmetric; two; point; distribution; characterization; constant; (zero); regression (search for similar items in EconPapers)
Date: 1979
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