
Accession Number : AD0687110
Title : A GENERALIZED UNIMODALITY.
Descriptive Note : Technical rept.,
Corporate Author : WISCONSIN UNIV MADISON DEPT OF STATISTICS
Personal Author(s) : Olshen,Richard A. ; Savage,Leonard J.
Report Date : 01 APR 1969
Pagination or Media Count : 25
Abstract : The paper introduces a definition  more exactly, a one parameter family of definitions  of unimodality for random objects taking values in a finite dimensional vector space. The possibility of a more general range space is briefly mentioned, and some special attention is given to the one dimensional case and its connections with ordinary unimodality. Two characterizations, or alternative definitions, of alphaunimodality are given. One of these is an extension of Khintchine's theorem to alphaunimodality. The other is related to an inequality discovered by Anderson for a type of unimodality stricter than nunimodality for an ndimensional vector space. In more than one dimension, the distribution of an alphaunimodal vector can be completely singular, but also it can be absolutely continuous. The densities of absolutely continuous alphaunimodal random vectors are characterized. The notion of alphaunimodality permits a little to be salvaged from the known disaster that sums of real, independent, unimodal random numbers need not be unimodal. (Author)
Descriptors : (*DISTRIBUTION THEORY, VECTOR SPACES), MEASURE THEORY, PROBABILITY, DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE