相关论文: The $m$th Gini index estimator: Unbiasedness for g…
In this paper, we introduce a novel flexible Gini index, referred to as the extended Gini index, which is defined through ordered differences between the $j$th and $k$th order statistics within subsamples of size $m$, for indices satisfying…
This paper examines the properties of the Gini coefficient estimator for gamma mixture populations and reveals the presence of bias. In contrast, we show that sampling from a gamma distribution yields an unbiased estimator, consistent with…
In this paper, we propose two new flexible Gini indices (extended lower and upper) defined via differences between the $i$-th observation, the smallest order statistic, and the largest order statistic, for any $1 \leqslant i \leqslant m$.…
This paper studies a class of rank-based inequality measures built from linear combinations of expected order statistics. The proposed framework unifies several well-known indices, including the classical Gini coefficient, the $m$th Gini…
In this paper, we derive a general representation for the expectation of the Gini coefficient estimator in terms of the Laplace transform of the underlying distribution, together with the mean and the Gini coefficient of its exponentially…
This paper analyzes the Gini coefficient estimator for zero-truncated Poisson populations, revealing the presence of bias, and provides a mathematical expression for the bias, along with a bias-corrected estimator, which is evaluated using…
The Gini index is a popular inequality measure with many applications in social and economic studies. This paper studies semiparametric inference on the Gini indices of two semicontinuous populations. We characterize the distribution of…
The Hoover index is a widely used measure of inequality with an intuitive interpretation, yet little is known about the finite-sample properties of its empirical estimator. In this paper, we derive a simple expression for the expected value…
This paper examines the finite-sample bias of estimators for the Theil and Atkinson indices, as well as for the variance-to-mean ratio (VMR), under the assumption that the population follows a finite mixture of gamma distributions with a…
We consider Gini's mean difference statistic as an alternative to the empirical variance in the settings of finite populations where simple random samples are drawn without replacement. In particular, we discuss specific (in the finite…
The Gini's mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini's index, denotes two times the area between the egalitarian…
The Gini index underestimates inequality for heavy-tailed distributions: for example, a Pareto distribution with exponent 1.5 (which has infinite variance) has the same Gini index as any exponential distribution (a mere 0.5). This is…
Currently, the high-precision estimation of nonlinear parameters such as Gini indices, low-income proportions or other measures of inequality is particularly crucial. In the present paper, we propose a general class of estimators for such…
The objective of this paper is to propose an unbiased ratio-type estimator for finite population mean when the variables are negatively correlated. Hartley and Ross[2] and Singh and Singh [6] estimators are identified as particular cases of…
We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index $\alpha\in(1,2)$).…
The inequality is computed through the so-called Gini index. The population is assumed to have the variable of interest distributed according to the Gamma probability distribution. The results show that the Gini index is reduced when the…
We study design-unbiased estimation of the finite-population total $\sum_{i=1}^N y_i$ when each outcome satisfies known bounds $y_i\in[a_i,b_i]$. For any sampling design with inclusion probabilities $\pi_i>0$, we prove a sharp lower bound…
The Gini index is a function that attempts to measure the amount of inequality in the distribution of a finite resource throughout a population. It is commonly used in economics as a measure of inequality of income or wealth. We define a…
This paper presents an analysis of the Theil and Atkinson index estimators for gamma populations, highlighting the presence of bias in both cases. Theoretical expressions for the biases are obtained, and bias-corrected estimators are…
Gini index is a widely used measure of economic inequality. This article develops a general theory for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width. Fixed sample size…