Ordered Random Variables have attracted several authors. The basic building block of Ordered Random Variables is Order Statistics which has several applications in extreme value theory and ordered estimation. The general model for ordered random variables, known as Generalized Order Statistics has been introduced relatively recently by Kamps (1995).

This book intended to cover the overview of unequal probability sampling and Generalization of Murthy's (1957) estimator. The researcher in the field of survey sampling can get benefit from this book. This book covers an overview of the unequal probability sampling, work done for Horvitz and Thompson (1952), Raj(1956) and Murthy (1957) estimators. Simulation and Empirical studies are conducted to discuss the performance of various available estimators for unequal probability sampling.

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.

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 and Thompson (1952) estimator. Some new estimators have been discussed alongside their design and model based study. The empirical comparison of proposed techniques has also been given with some well known estimation techniques of unequal probability sampling.

The development of estimators of population parameters based on two-phase sampling schemes has seen a dramatic increase in the past decade. Various authors have developed estimators of population mean of study variables using either single or two auxiliary variables. The present volume is a comprehensive collection of estimators available in single and two phase sampling. The book covers estimators which utilize information on single, two and multiple auxiliary variables of both quantitative and qualitative nature. The estimators discussed in the monograph are based upon different mechanisms of availability of auxiliary information, termed as Full, Partial and No Information. Multivariate Estimators in survey sampling are also discussed in the book. Two-Phase Sampling will prove an invaluable point of reference for researchers working in the field of survey sampling in general and in the field of two-phase sampling in particular.