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Simple proofs of two results on convolutions of unimodal distributions

DSpace at IIT Bombay

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Title Simple proofs of two results on convolutions of unimodal distributions
 
Creator PURKAYASTHA, S
 
Subject convolution
khintchine's representation
symmetry
unimodality
 
Description We give simple proofs of two results about convolutions of unimodal distributions. The first of these results states that the convolution of two symmetric unimodal distributions on R is unimodal. The other result states that symmetrization of a unimodal random variable gives a symmetric unimodal random variable. Both our proofs avoid Khintchine's representation of a random variable that is unimodal about zero, and use the integral representation of the expectation of a non-negative random variable with its tail probability as the integrand. (C) 1998 .
 
Publisher ELSEVIER SCIENCE BV
 
Date 2011-07-26T17:01:20Z
2011-12-26T12:55:18Z
2011-12-27T05:44:04Z
2011-07-26T17:01:20Z
2011-12-26T12:55:18Z
2011-12-27T05:44:04Z
1998
 
Type Article
 
Identifier STATISTICS & PROBABILITY LETTERS, 39(2), 97-100
0167-7152
http://dx.doi.org/10.1016/S0167-7152(98)00013-3
http://dspace.library.iitb.ac.in/xmlui/handle/10054/6970
http://hdl.handle.net/10054/6970
 
Language en