Goodness-of-fit testing for the Pareto type-I distribution based on a mean residual life characterization
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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BibTeX
@misc{nila2026goodnessoffit,
title = {{Goodness-of-fit testing for the Pareto type-I distribution based on a mean residual life characterization}},
author = {Shivshankar Nila and Ishapathik Das and N. Balakrishna},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04933},
eprint = {2609.04933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04933},
}
RIS
TY - UNPB
TI - Goodness-of-fit testing for the Pareto type-I distribution based on a mean residual life characterization
AU - Shivshankar Nila
AU - Ishapathik Das
AU - N. Balakrishna
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04933
UR - https://arxiv.org/abs/2609.04933
AB - 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.
ER -