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arXiv2026

A New Generalized Birnbaum-Saunders Regression Model: Inference, Diagnostics, and Applications

The Birnbaum-Saunders (BS) distribution has become a widely used model for positive and asymmetric continuous data. Several extensions of the BS distribution have been proposed, including regression formulations that relate its parameters to covariates. In this paper, we introduce a new regression model for the Generalized Birnbaum-Saunders (GBS) distribution, an extension that has received limited attention in the literature despite offering a stronger physical interpretation. The proposed framework follows the structure of Generalized Additive Models for Location, Scale, and Shape (GAMLSS), allowing covariate effects to be incorporated into all three parameters of the distribution, thereby providing greater flexibility for modeling data. In particular, one of the model parameters has a direct interpretation as the median of the response variable, facilitating the interpretation of covariate effects on the conditional median. Parameter estimation is performed via maximum likelihood, and hypothesis tests are proposed based on the Wald test. The proposed regression model is implemented in R through the gamlss package, allowing access to a broad range of tools for model fitting, diagnostics, and assessment. Monte Carlo simulation studies are conducted to investigate the finite-sample performance of the maximum likelihood estimators. The results show that the estimators exhibit desirable properties, with bias decreasing and efficiency increasing as sample size grows. Additionally, the behavior of the Wald test is investigated, showing good performance for moderate to large sample sizes. Finally, two applications to real data illustrate the practical usefulness of the proposed GBS regression model, demonstrating that it is a flexible alternative for modeling positive and asymmetric data compared to the BS model

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arXiv2025

Stability Analysis and Local Influence Diagnostics for an Extreme-Value Regression Model of Anomalous Wind Gusts

Extreme events in complex physical systems, such as anomalous wind gusts, often cause significant material and human damage. Their modeling is crucial for risk assessment and understanding the underlying dynamics. In this work, we introduce a local influence analysis to assess the stability of a class of extreme-value Birnbaum-Saunders regression models, which are particularly suited for analyzing such data. The proposed approach uses the conformal normal curvature (CNC) of the log-likelihood function to diagnose the influence of individual observations on the postulated model. By examining the eigenvalues and eigenvectors associated with the CNC, we identify influential data points-physical events that disproportionately affect the model's parameters. We illustrate the methodology through a simulation study and apply it to a time series of wind gust data from Itajai, Brazil, where a severe event caused multiple damages and casualties. Our approach successfully pinpoints this specific event as a highly influential observation and quantifies its impact on the fitted model. This work provides a valuable diagnostic tool for physicists and data scientists working with extreme-value models of complex natural phenomena.

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