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arXiv · 2609.04933

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

Shivshankar Nila·Ishapathik Das·N. Balakrishna
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Abstract

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.

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Shivshankar Nila, Ishapathik Das, N. Balakrishna. 2026-09-04. Goodness-of-fit testing for the Pareto type-I distribution based on a mean residual life characterization. https://arxiv.org/abs/2609.04933

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