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The Murthy (1957) estimator has been extensively studied by various
authors. The design based variance of the estimator has been
studied by the various survey statisticians. The modifications of
the Murthy (1957) estimator has been proposed by Shahbaz (2004)
alongside the design based study. The model based study of the
estimator has been presented in this monograph. We have also
studied the stability of the variance estimator of the modified
Murthy (1957) estimator under the linear super-population model. It
has been observed that the anticipated variance of the modified
Murthy (1957) estimator achieves the Godambe-Joshi (1965) lower
bound and the variance estimator is stable.
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