
Accession Number : AD0697288
Title : GPEAKEDNESS COMPARISONS FOR RANDOM VECTORS.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS
Personal Author(s) : Mudholkar,Govind S.
Report Date : 07 NOV 1969
Pagination or Media Count : 18
Abstract : The concept of Gpeakedness is proposed as a generalization of Z.W. Birnbaum's (Ann. Math. Statist., 19, 1948) definition of peakednesscomparisons of random variables and of an extension of this definition to random vectors by S. Sherman (Ann. Math. Statist., 27, 1956). If G is a group of linear transformations of R superscript n with unit determinant and 0 sub G is the set of points invariant under G then a random vector X is defined to be more Gpeaked than another random vector Y if Pr(X epsilon E) = or > Pr(Y epsilon E) for every compact, convex, Ginvariant set E. If X sub i is more Gpeaked than Y sub i, i=1,2, then it is proved that under certain conditions X sub 1 + X sub 2 is more Gpeaked than Y sub 1 + Y sub 2. As a byproduct, an inequality for integrals due to Mudholkar (Proc. Amer. Math. Soc. 17, 1966) is generalized. (Author)
Descriptors : (*RANDOM VARIABLES, PROBABILITY DENSITY FUNCTIONS), TRANSFORMATIONS(MATHEMATICS), CONVEX SETS, INTEGRALS, INEQUALITIES, THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE