As we all know that sampling with unequal probability plays most important role in large scale sample surveys, therefore in this monograph some recent developments regarding this topic has been discussed. Moreover since joint probability is difficult calculate therefore some approximations of the joint probability have been derived. Special attention has been given to general theory of arbitrary probability. For this theory sampling with replacement and without replacement are the special cases of this general theory. Generalized Murthy estimator has also been discussed in details.

Unequal Probability Sampling has been efficiently used for estimation of population characteristics. Several developments have been made from time to time to increase the precision of estimates. In this book we present some new methods of estimation in unequal probability sampling. Some selection procedures have been discussed for use with the Horvitz and Thompson (1952) estimator. We have also proposed a general selection procedure which yields several selection procedures as special case. We have also discussed the method of developing the approximations for variance formulae for Horvitz...

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)...