arXiv subjects

S. M. Sunoj

Publications and source records attributed to S. M. Sunoj.

7 recordsLinked to original sources

arXiv2026

A Conditional Quantile Approach to Vector-Valued Bivariate Lorenz Surfaces: Properties and Applications

The Lorenz curve is a fundamental tool for measuring inequality, but its extension to multivariate settings remains challenging due to the complex dependence structure among variables and the need to capture directional aspects of inequality. In this paper, we introduce a novel vector-valued bivariate Lorenz surface (VBLS) based on conditional distributions and conditional quantile functions. Unlike existing symmetric bivariate Lorenz surfaces, the proposed VBLS effectively captures the directional inequality arising from the conditional dependence between two variables. We establish several fundamental properties of the proposed surface and investigate its mathematical properties. The corresponding egalitarian surface is defined, leading to the development of associated vector-valued bivariate Gini measures for quantifying inequality. We further derive characterization results that demonstrate the uniqueness of the proposed VBLS within the underlying distributional framework. Nonparametric estimators of the VBLS are developed and their finite-sample performance is evaluated through a simulation study. The usefulness of the proposed methodology is also illustrated with applications to income inequality and actuarial data.

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arXiv2026

On Some Multivariate Extensions to Zenga Curve: Properties and Applications

Measures of inequality are often limited in their ability to capture multidimensional aspects that arise from the joint distribution of multiple socio-economic variables. In this paper, we develop bivariate extensions of the Zenga inequality measure using bivariate quantile functions. We propose new bivariate Zenga surfaces and study their theoretical properties. A vector-valued bivariate Zenga curve is also introduced to provide a more detailed characterization of inequality. A non-parametric estimator is proposed and methods are evaluated through simulation studies and applied to the analysis of digital inequality across countries using indicators such as broadband penetration and digital literacy. The results highlight the effectiveness of the proposed framework in capturing multidimensional inequality.

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arXiv2025

Fractional cumulative Residual Inaccuracy in the Quantile Framework and its Appications

Fractional cumulative residual inaccuracy (FCRI) measure allows to determine regions of discrepancy between systems, depending on their respective fractional and chaotic map parameters. Most of the theoretical results and applications related to the FCRI of the lifetime random variable are based on the distribution function approach. However, there are situations in which the distribution function may not be available in explicit form but has a closed-form quantile function (QF), an alternative method of representing a probability distribution. Motivated by these, the present study is devoted to introduce a quantile-based FCRI and study its various properties. We also deal with non-parametric estimation of quantile-based FCRI and examine its validity using simulation studies and illustrate its usefulness in measuring the discrepancy between chaotic systems and in measuring the discrepancy in two different time regimes using Nifty 50 dataset.

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arXiv2025

Revisiting poverty measures using quantile functions

In this article we redefine various poverty measures in literature in terms of quantile functions instead of distribution functions in the prevailing approach. This enables provision for alternative methodology for poverty measurement and analysis along with some new results that are difficult to obtain in the existing framework. Several flexible quantile function models that can enrich the existing ones are proposed and their utility is demonstrated for real data.

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arXiv2025

A quantile-based bivariate distribution

In this paper we present a flexible bivariate distribution specified by a quantile function. The distribution contains as special cases new bivariate exponential, Pareto I, Pareto II, beta, power, log logistic and uniform distributions and also can approximate many other continuous models. Various $L$-moment based properties of the distribution such as covariance, coskewness, cokurtosis, $L$-correlation, etc are discussed. The distribution is used to model two real data sets.

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arXiv2025

Fractional Cumulative Residual Entropy in the Quantile Framework and its Applications in the Financial Data

Fractional cumulative residual entropy (FCRE) is a powerful tool for the analysis of complex systems. Most of the theoretical results and applications related to the FCRE of the lifetime random variable are based on the distribution function approach. However, there are situations in which the distribution function may not be available in explicit form but has a closed-form quantile function (QF), an alternative method of representing a probability distribution. Motivated by this, in the present study we introduce a quantile-based FCRE, its dynamic version and their various properties and examine their usefulness in different applied fields.

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arXiv2024

On weighted failure rate, its means and associated quantile version

In this paper, we define weighted failure rate and their different means from the stand point of an application. We begin by emphasizing that the formation of n independent component series system having weighted failure rates with sum of weight functions being unity is same as a mixture of n distributions. We derive some parametric and non-parametric characterization results. We discuss on the form invariance property of baseline failure rate for a specific choice of weight function. Some bounds on means of aging functions are obtained. Here, we establish that weighted IFRA class is not closed under formation of coherent systems unlike the IFRA class. An interesting application of the present work is credited to the fact that the quantile version of means of failure rate is obtained as a special case of weighted means of failure rate.

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