Accession Number : AD0697288
Title : G-PEAKEDNESS 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 G-peakedness is proposed as a generalization of Z.W. Birnbaum's (Ann. Math. Statist., 19, 1948) definition of peakedness-comparisons 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 G-peaked than another random vector Y if Pr(X epsilon E) = or > Pr(Y epsilon E) for every compact, convex, G-invariant set E. If X sub i is more G-peaked than Y sub i, i=1,2, then it is proved that under certain conditions X sub 1 + X sub 2 is more G-peaked 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