Slashed Lomax Distribution and Regression Model

In this article, the slashed Lomax distribution is introduced, which is an asymmetric distribution and can be used for fitting thick-tailed datasets. Various properties are explored, such as the density function, hazard rate function, Renyi entropy, r-th moments, and the coefficients of the skewness and kurtosis. Some useful characterizations of this distribution are obtained. Furthermore, we study a slashed Lomax regression model and the expectation conditional maximization (ECM) algorithm to estimate the model parameters. Simulation studies are conducted to evaluate the performances of the proposed method. Finally, two sets of data are applied to verify the importance of the slashed Lomax distribution.

A CLASS OF MIXTURE OF EXPERTS MODELS FOR GENERAL INSURANCE: APPLICATION TO CORRELATED CLAIM FREQUENCIES

This paper focuses on the estimation and application aspects of the Erlang count logit-weighted reduced mixture of experts model (EC-LRMoE), which is a fully flexible multivariate insurance claim frequency regression model. We first prove the identifiability property of the proposed model to ensure that it is a suitable candidate for statistical inference. An expectation conditional maximization (ECM) algorithm is developed for efficient model calibrations. Three simulation studies are performed to examine the effectiveness of the proposed ECM algorithm and the versatility of the proposed model. The applicability of the EC-LRMoE is shown through fitting an European automobile insurance data set. Since the data set contains several complex features, we find it necessary to adopt such a flexible model. Apart from showing excellent fitting results, we are able to interpret the fitted model in an insurance perspective and to visualize the relationship between policyholders’ information and their risk level. Finally, we demonstrate how the fitted model may be useful for insurance ratemaking.

Compact Belief Rule Base Learning for Classification with Evidential Clustering

The belief rule-based classification system (BRBCS) is a promising technique for addressing different types of uncertainty in complex classification problems, by introducing the belief function theory into the classical fuzzy rule-based classification system. However, in the BRBCS, high numbers of instances and features generally induce a belief rule base (BRB) with large size, which degrades the interpretability of the classification model for big data sets. In this paper, a BRB learning method based on the evidential C-means clustering (ECM) algorithm is proposed to efficiently design a compact belief rule-based classification system (CBRBCS). First, a supervised version of the ECM algorithm is designed by means of weighted product-space clustering to partition the training set with the goals of obtaining both good inter-cluster separability and inner-cluster pureness. Then, a systematic method is developed to construct belief rules based on the obtained credal partitions. Finally, an evidential partition entropy-based optimization procedure is designed to get a compact BRB with a better trade-off between accuracy and interpretability. The key benefit of the proposed CBRBCS is that it can provide a more interpretable classification model on the premise of comparative accuracy. Experiments based on synthetic and real data sets have been conducted to evaluate the classification accuracy and interpretability of the proposal.