A Multivariate Log-Linear Model for Birnbaum-Saunders Distributions

In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum-Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.

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“…() and Marchant et al. (, ). Work on some of these issues is currently in progress and we hope to report some findings in a future paper.…”

Section: Discussion Conclusion and Future Researchmentioning

confidence: 98%

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

et al. 2017

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“…In addition, influence diagnostic tools can be extended to more general Birnbaum-Saunders ACD models, such as those based on scale mixture of normals or versions of extreme value; see Leiva et al (2016a). Furthermore, multivariate models can also be explored; see Marchant et al (2016a). Work on some of these issues is currently in progress and we hope to report some findings in future papers.…”

Section: Discussionmentioning

confidence: 99%

Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data

et al. 2017

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Modern financial markets now record the precise time of each stock trade, along with price and volume, with the aim of analysing the structure of the times between trading events -leading to a big data problem. In this paper, we propose and compare two Birnbaum-Saunders autoregressive conditional duration models specified in terms of time-varying conditional median and mean durations. These models provide a novel alternative to the existing autoregressive conditional duration models due to their flexibility and ease of estimation. Influence diagnostic tools are developed to allow goodness-of-fit assessment and to detect departures from assumptions, including the presence of outliers and influential cases. Both global and local influence tools are considered based on the parameter estimates under different perturbation schemes. A thorough Monte Carlo study is presented to evaluate the performance of the maximum likelihood estimators, and the forecasting ability of the models is assessed using the traditional and density forecast evaluation techniques. The Monte Carlo study suggests that the parameter estimators are asymptotically unbiased, consistent and normally distributed. Finally, a full analysis of a real-world financial transaction data set, from the German DAX in 2016, is presented to illustrate the proposed approach and to compare the fitting and forecasting performances with existing models in the literature. One case related to the duration time is identified as potentially influential, but its removal does not change resulting inferences demonstrating the robustness of the proposed approach. Fitting and forecasting performances favor the proposed models and, in particular, the median-based approach gives additional protection against outliers, as expected.

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“…Furthermore, acceptance regions for goodness of fit based on L-moments are also an important issue to be considered [52]. Incorporation of censored data, multivariate versions of value extreme Birnbaum-Saunders distributions, and their modeling and diagnostics are also of interest [39,40] in the context of L-moments. As future research, all of these issues are being explored by the authors.…”

Section: Discussionmentioning

confidence: 99%

L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

Lillo

Leiva

Nicolis

et al. 2016

Journal of Applied Statistics

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Understanding patterns in the frequency of extreme natural events, such as earthquakes, is important as it helps in the prediction of their future occurrence and hence provides better civil protection. Distributions describing these events are known to be heavy tailed and positive skew making standard distributions unsuitable for such a situation. The Birnbaum-Saunders distribution and its extreme value version have been widely studied and applied due to their attractive properties. We derive L-moment equations for these distributions and propose novel methods for parameter estimation, goodness-of-fit assessment and model selection. A simulation study is conducted to evaluate the performance of the L-moment estimators, which is compared to that of the maximum likelihood estimators, demonstrating the superiority of the proposed methods. To illustrate these methods in a practical application, a data analysis of real-world earthquake magnitudes, obtained from the global centroid moment tensor catalogue during 1962-2015, is carried out. This application identifies the extreme value Birnbaum-Saunders distribution as a better model than classic extreme value distributions for describing seismic events.

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A Multivariate Log-Linear Model for Birnbaum-Saunders Distributions

Cited by 57 publications

References 37 publications

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data

L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

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