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.
We study from a finite-sample viewpoint the problem of building tests and simultaneous confidence bands for cumulative distribution functions (CDFs), continuous or discrete. We emphasize procedures based on reweighted empirical distribution function (EDF) with shrinking bandwidths in the tails of the distribution. Sinc...
We propose a class of extended generalized Pareto models for right-censored survival data, with particular emphasis on tail inference and long-term extrapolation. Our framework integrates extreme value theory and survival analysis, combining a generalized Pareto distribution with a flexible perturbation distribution on...
Eduardo Janotti, L. Henriques-Rodrigues, A. C. D. de Lima· 0 citations
Expectiles have received increasing attention as a market risk measure that is both coherent and elicitable. They are defined as a least squares analog to quantiles. Their estimation from heavy-tailed loss data in an extreme value framework is an important and difficult problem, especially when the target tail expectil...
Yasser Abbas, A. Daouia, B. Nemouchi et al.· Econometric Theory· 0 citations
The Unit Inverse Lomax Distribution (UILxD) is introduced as a new statistical model tailored for data within the unit interval. This paper explores the theoretical framework of UILxD, presenting closed form expressions for its probability density function, cumulative distribution function, survival function, hazard ra...
S. T, B. P.· Brazilian Journal of Biometr...· 0 citations
Recent advancements in distributional theory have increasingly focused on constructing flexible probability models capable of capturing complex real-world phenomena more effectively. Addressing this methodological need, this study introduces the Fréchet Weibull distribution, a novel extension of the classical Weibull m...
Mohammed Sa'ad, K. Lasisi, Abubakar Bishir et al.· African Journal of Advances...· 0 citations
Abstract This article develops a methodology for the meta-analysis of stage life testing experiments, combining data from s independent tests. Each experiment involves two stress levels, with the lifetime of experimental units at each level following an inverse Weibull distribution. The Khamis–Higgins model is used to...
