Hindawi Publishing Corporation ISRN Probability and Statistics Volume 2013, Article ID 659580, 14 pages http://dx.doi.org/10.1155/2013/659580 Research Article Estimates of Inequality Indices Based on Simple Random, Ranked Set, and Systematic Sampling Pooja Bansal, Sangeeta Arora, and Kalpana K. Mahajan Department of Statistics, Panjab University, Chandigarh 160014, India Correspondence should be addressed to Sangeeta Arora; sarora131@gmail.com Received 16 June 2013; Accepted 2 August 2013 Academic Editors: X. Dang and S. Lototsky Copyright © 2013 Pooja Bansal et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Gini index, Bonferroni index, and Absolute Lorenz index are some popular indices of inequality showing diferent features of inequality measurement. In general simple random sampling procedure is commonly used to estimate the inequality indices and their related inference. Te key condition that the samples must be drawn via simple random sampling procedure though makes calculations much simpler but this assumption is ofen violated in practice as the data does not always yield simple random sample. Nonsimple random samples like Ranked set sampling or stratifed sampling are gaining popularity for estimating these indices. Te purpose of the present paper is to compare the efciency of simple random sample estimates of inequality indices with their nonsimple random counterparts. Monte Carlo simulation technique is applied to get the results for some specifc distributions. 1. Introduction Lorenz curve [1] and the associated Gini index [2] are one of the most popular and frequently used tools to measure income inequality. Certain other variants of Lorenz curve, namely, Generalized Lorenz curve [3], Absolute Lorenz curve [4], Bonferroni curve [5], and Comic curves [3, 6] and associated inequality indices, that is, Generalized Lorenz index, Absolute Lorenz index, Bonferroni index, and Comic index, are some of the popular alternatives to Gini index used to study certain specialized features of inequality. In practice, mostly the simple random sampling procedure is used to derive the statistical inference or obtaining the sample estimates of these inequality measures. Te key condition that the samples must be drawn via simple random sampling procedure though makes calculations much simpler but this assumption is ofen violated in practice as the data does not always yield simple random sample. For example, in India the socioeconomic data collected by the National Sample Survey Organization (NSSO) is not drawn through simple random sampling but follows two-stage stratifed sampling techniques. Also in the United States, commonly used income and earnings data, such as the Current Population Survey (CPS) and the Panel Study of Income Dynamics (PSID), are all multistage random samples, where simple random sampling is not the only method applied at each stage. One may quote stratifed sampling, cluster sampling, multistage cluster sampling, and so forth, as alternatives to simple random sampling while estimating inequality indices [7]. Besides, these available traditional sampling methods, the method of Ranked set sampling (RSS), have also gained popularity in the literature for estimating parameters like population mean and variance and its associated statistical inference. Tis RSS method of sampling is proved to be more efcient than simple random sampling [8]. Tus, the RSS technique may also be extended to obtain the sample estimates of these inequality measures, and it will be extended to compare the efciency of RSS with simple random and other sampling estimates as applied to inequality measures. [9] have given the comparison of ranked set sample estimate of Gini index with simple random sampling for a non- standard Lorenz curve equation using simulation technique and are not true in general as no standard distributions are considered. Te purpose of the present work is to compare the nonsimple random estimates of the inequality measures