Suppose a sample of size n is drawn from a mixture distribution
where component distribution functions
and
are such that
is stochastically smaller than
. Out of these n observations, the first
smallest and last
largest observations could have, respectively, come from distributions
and
. It is proposed to estimate parameters of F(x) using least-squares type criterion given in terms of quantile functions of
,
and a quantile function obtained using a convex combination of quantile functions of
and
. Extensive numerical results that compare the mean squared errors of these newly proposed estimators of different parameters of a mixture of exponential distributions with those of standard estimators, such as maximum likelihood and moment estimators etc., obtained using individual components
and
of the given mixture distribution are given. It is to be highlighted that these newly proposed estimators outperform the standard ones for various values of
and
and δ. Similar results are obtained by comparing generalized variance of a bivariate vector made up of new estimators of two exponential distributions with that of a bivariate vector formed using existing set of estimators for two cases, namely, (i) δ is known and (ii) δ is unknown and they are also found to be encouraging.
