arXiv subjects

Marco Bee

Publications and source records attributed to Marco Bee.

3 recordsLinked to original sources

arXiv2026

Flexible modeling of bimodal distributions via skewed-$t$ mixtures

We propose a mixture of location-scale skewed-$t$ distributions to fit bimodal, skewed and heavy-tailed data. In particular, the mixture is based on the skewed-$t$ distribution by Fern\'andez and Steel (1998), so that the model-building procedure can be easily extended to mixtures of other symmetric distributions. After studying the properties of the mixture, we develop a maximum likelihood estimation approach via the EM algorithm and a likelihood ratio test of the null hypothesis of no skewness in any given component. A simulation-based comparison to a recently proposed mixture of g-and-h distributions suggests that the performance of the proposed model is excellent, in terms of both estimation precision in well-specified setups and modeling capability in mis-specified frameworks. Fitting the model to the Standard & Poor's 500 distortion allows us to confirm the bimodality of its distribution, with the implication that the US stock market has historically been in bearish or bullish conditions, rather than near its fundamental value.

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arXiv2025

Modeling and estimating skewed and heavy-tailed populations via unsupervised mixture models

We develop a mixture model for non-negative, heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the distribution, and a Pareto-type tail, aimed at accommodating the largest observations, since the lognormal often decays too fast. Given that the tail is modeled by a zero-location Generalized Pareto distribution, the model is fully unsupervised, i.e. no threshold needs to be chosen. We show that maximum likelihood estimation can be performed by means of the EM algorithm and that the model is quite flexible in fitting data from different data-generating processes. Simulation experiments and a real-data application to automobiles claims suggest that the approach is equivalent in terms of goodness-of-fit, but easier to estimate, with respect to two existing distributions with similar features. All the methods are implemented in the R package lognGPD, available on CRAN.

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arXiv2022

Unsupervised Mixture Estimation via Approximate Maximum Likelihood based on the Cram\'er - von Mises distance

Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate numerically an intractable normalizing constant. In such a setup, simulation-based estimation methods are an appealing alternative. The approximate maximum likelihood estimation (AMLE) approach is employed. It is a general method that can be applied to mixtures with any component densities, as long as simulation is feasible. The focus is on the dynamic lognormal-generalized Pareto distribution, and the Cram\'er - von Mises distance is used to measure the discrepancy between observed and simulated samples. After deriving the theoretical properties of the estimators, a hybrid procedure is developed, where standard maximum likelihood is first employed to determine the bounds of the uniform priors required as input for AMLE. Simulation experiments and two real-data applications suggest that this approach yields a major improvement with respect to standard maximum likelihood estimation.

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