Affiliations: [a] Department of Mathematics, IIT Bombay, Mumbai, India | [b] Department of Statistics, University of Pune, Pune, India
Correspondence:
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Corresponding author: S.V. Sabnis, Department of Mathematics, IIT Bombay, Mumbai, India. Tel.: +91 22 2576 7474; Fax: +91 22 2576 3480; E-mail: svs@math.iitb.ac.in.
Abstract: Suppose a sample of size n is drawn from a mixture distribution F(x)=δF1(x)+(1−δ)F2(x) where component distribution functions F1(x) and F2(x) are such that F1(x) is stochastically smaller than F2(x). Out of these n observations, the first r1 smallest and last r2 largest observations could have, respectively, come from distributions F1(x) and F2(x). It is proposed to estimate parameters of F(x) using least-squares type criterion given in terms of quantile functions of F1(x), F2(x) and a quantile function obtained using a convex combination of quantile functions of F1(x) and F2(x). 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 F1(x)=1−exp(−λ1x) and F2(x)=1−exp(−λ2x) 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 r1 and r2 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.
