Abstract
This paper deals with the estimation of
R =
P(
Y <
X) when
Y and
X are two independent but not identically distributed Burr-type
X random variables. Maximum likelihood, Bayes and empirical Bayes techniques are used for this purpose. Monte-Carlo simulation is carried out to compare the three methods of estimation. Also, two characterizations of the Burr-type
X distribution are presented. The first characterization is based on the recurrence relationships between two successively conditional moments of a certain function of the random variable, whereas the second one is given by the conditional variance of that function.