Sangeeta Arora

Testing Homogeneity of Gini Indices Against Simple-Ordered Alternative

Gini index is one of the most popular indices employed for measuring inequality in income and wealth. In this article, we propose a multi-sample test for testing Gini indices against simple-ordered alternatives. The exact critical points through simulation were computed for the proposed test in case of two-parameter exponential distribution; however, the proposed test can be applied even in case of other distributions like Pareto, Weibull, etc. Construction of simultaneous one-sided confidence intervals (SOCIs) was proposed along with an illustration. Power of the test is computed and some power comparisons are also made.

Testing for Generalized Lorenz Dominance

The Generalized Lorenz dominance can be used to take account of differences in mean income as well as income inequality in case of two income distributions possessing unequal means. Asymptotically distribution-free and consistent tests have been proposed for comparing two generalized Lorenz curves in the whole interval [p1, p2] where 0 < p1 < p2 < 1. Size and power of the test has been derived.

A class of nonparametric tests for testing homogeneity of variances against ordered alternatives based on subsample extrema

SummaryA class of nonparametric test statistics for several sample scale problem is proposed by considering extrema of subsamples of size c. The proposed class of statistics has the advantage of not requiring the several distribution functions to have a common median, but rather any common quantile of order α, 0 ≤ α ≤1, (not necessarily 1/2) which is assumed to be known. The proposed class of tests is compared with other known tests already existing in the literature in the Pitman asymptotic relative efficiency sense for different distributions. Some results of Monte Carlo power study are also presented.

Bayesian estimation for Gini index and a poverty measure in case of pareto distribution using Jeffreys' prior

Bayes estimators are obtained in case of Pareto distribution for its shape parameter, mean income, Gini index and a Poverty measure for both censored and complete setup. The said estimators are obtained using Jeffreys’ non-informative invariant prior and the extension of Jeffreys’ prior information. Using simulation techniques, the relative efficiency of proposed estimators with the existing estimators using two-parameter exponential prior is obtained. It turns out that the Bayesian method with Jeffreys’ non-informative invariant prior results in smaller expected loss function as compared to existing estimators using two-parameter exponential prior.

Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function

Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function.

Predicting air quality using ARIMA, ARFIMA and HW smoothing

Air quality indices (AQIs), used to classify and report the ambient air quality all across the world, computed for pol- lutants SPM, RSPM, NO2 and SO2 for the city Chandigarh using 24-hourly data revealed, RSPM as one of the main responsible air pollutants. Three time series models viz. ARIMA, ARFIMA and Holt and Winters (HW) smoothing techniques are employed to assess and predict the air quality status with respect to responsible pollutant RSPM. Various model selection criteria like Mean Absolute Error, Mean Absolute Percentage Error, Root Mean Square Error, and Bias corrected Akaikes information criterion (AICC) suggested ARFIMA as the appropriate model. Different long memory tests also justify the use of ARFIMA model and its comparison with ARIMA and HW smoothing techniques yield improved estimators/predictors for the responsible pollutant RSPM.

Estimates of Inequality Indices Based on Simple Random, Ranked Set, and Systematic Sampling

Gini index, Bonferroni index, and Absolute Lorenz index are some popular indices of inequality showing different features of inequality measurement. In general simple random sampling procedure is commonly used to estimate the inequality indices and their related inference. The key condition that the samples must be drawn via simple random sampling procedure though makes calculations much simpler but this assumption is often violated in practice as the data does not always yield simple random sample. Nonsimple random samples like Ranked set sampling or stratified sampling are gaining popularity for estimating these indices. The purpose of the present paper is to compare the efficiency 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 specific distributions.

Confidence bands and statistical inference for conditional coefficient of variation in case of crossing Lorenz curves

When Lorenz curves cross, conditional coefficient of variation curve can be used to test the inequality dominance. In the present paper, confidence bands are provided for conditional coefficient of variation curve. Based on these confidence bands a multiple comparison test is proposed for testing the dominance of conditional coefficient of variation curve. The power of the test is computed and a real life illustration is given at the end.