On the right spread order of convolutions of heterogeneous exponential random variables

Authors:
Subhash Kochar;Maochao Xu
Affiliations:
Department of Mathematics and Statistics, Portland State University, Portland, OR 97201, USA;Department of Mathematics and Statistics, Portland State University, Portland, OR 97201, USA
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

A sufficient condition for comparing convolutions of heterogeneous exponential random variables in terms of right spread order is established. As a consequence, it is shown that a convolution of heterogeneous independent exponential random variables is more skewed than that of homogeneous exponential random variables in the sense of NBUE order. This gives a new insight into the distribution theory of convolutions of independent random variables. A sufficient condition is also derived for comparing such convolutions in terms of Lorenz order.