arXiv subjects

Shivshankar Nila

Publications and source records attributed to Shivshankar Nila.

4 recordsLinked to original sources

arXiv2026

Goodness-of-fit testing for the Pareto type-I distribution based on a mean residual life characterization

The statistical analysis of heavy-tailed data has received considerable attention because extreme observations frequently arise in many practical applications. The Pareto type-I distribution is a fundamental heavy-tailed model used in economics, finance, actuarial science, insurance, reliability, and extreme value analysis. In this paper, we propose novel goodness-of-fit tests for the Pareto distribution using a mean residual life characterization. The test statistic is constructed using U-statistic theory, and its asymptotic behaviour is established under both the null and alternative hypotheses. Its finite-sample performance is evaluated through Monte Carlo simulations using maximum-likelihood and method-of-moments estimation and compared with existing tests. The results show that the proposed test controls the nominal significance level and performs competitively in terms of power across a broad range of alternatives. Finally, the proposed methodology is illustrated using the Danish fire insurance loss and pollution datasets.

stat.ME↗

arXiv2026

Robust Modeling of Extremes in the Presence of Inliers with Enhanced Tail Estimation

Extreme value theory provides a fundamental framework for modeling rare and extreme events; however, threshold selection remains a persistent challenge, particularly in the presence of inliers such as instantaneous or early failures. Such observations commonly arise in applications including reliability studies and environmental data, where clusters of observations near the origin or at the origin can substantially distort classical threshold selection procedures and tail inference. In this paper, we propose a robust modeling framework that accounts for inliers, extremes, and the tail proportion. Parameter estimation is carried out using maximum likelihood. The proposed methodology is compared with classical numerical and graphical diagnostic tools, including the mean excess plot, parameter stability plot, Hill plot, and Pickands plot, as well as existing extreme value mixture models. The theoretical properties of the proposed model are established, and its performance is evaluated through extensive Monte Carlo simulations and real-data applications. The results demonstrate that the proposed methodology provides more accurate threshold estimation and more reliable extreme-value inference in the presence of inliers compared with existing classical approaches. Overall, the proposed methodology provides more accurate threshold estimation and tail inference in the presence of inliers, addressing key limitations of existing methods.

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arXiv2026

Modeling Extreme Events in the Presence of Inlier: A Mixture Approach

In many random phenomena, such as life-testing experiments and environmental data (like rainfall data), there are often positive values and an excess of zeros, which create modeling challenges. In life testing, immediate failures result in zero lifetimes, often due to defects or poor quality, especially in electronics and clinical trials. These failures, called zero inliers, are difficult to model using standard approaches. When studying extreme values in the above scenarios, a key issue is selecting an appropriate threshold for accurate tail approximation of the population using asymptotic models. While some extreme value mixture models address threshold estimation and tail approximation, conventional parametric and non-parametric bulk and generalised Pareto distribution (GPD) approaches often neglect inliers, leading to suboptimal results. This paper introduces a framework for modeling extreme events and inliers using the GPD, addressing threshold uncertainty and effectively capturing inliers at zero. The model's parameters are estimated using the maximum likelihood estimation (MLE) method, ensuring optimal precision. Through simulation studies and real-world applications, we demonstrate that the proposed model significantly outperforms the traditional methods, which typically neglect inliers at the origin.

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arXiv2026

A Flexible Modeling of Extremes in the Presence of Inliers

Many random phenomena, including life-testing and environmental data, show positive values and excess zeros, which pose modeling challenges. In life testing, immediate failures result in zero lifetimes, often due to defects or poor quality, especially in electronics and clinical trials. These failures, called inliers at zero, are difficult to model using standard approaches. The presence and proportion of inliers may influence the accuracy of extreme value analysis, bias parameter estimates, or even lead to severe events or extreme effects, such as drought or crop failure. In such scenarios, a key issue in extreme value analysis is determining a suitable threshold to capture tail behaviour accurately. Although some extreme value mixture models address threshold and tail estimation, they often inadequately handle inliers, resulting in suboptimal results. Bulk model misspecification can affect the threshold, extreme value estimates, and, in particular, the tail proportion. There is no unified framework for defining extreme value mixture models, especially the tail proportion. This paper proposes a flexible model that handles extremes, inliers, and the tail proportion. Parameters are estimated using maximum likelihood estimation. Compared the proposed model estimates with the classical mean excess plot, parameter stability plot, and Pickands plot estimates. Theoretical results are established, and the proposed model outperforms traditional methods in both simulation studies and real data analysis.

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