A NEW MULTIVARIATE ZERO-INFLATED HURDLE MODEL WITH APPLICATIONS IN AUTOMOBILE INSURANCE

The fact that a large proportion of insurance policyholders make no claims during a one-year period highlights the importance of zero-inflated count models when analyzing the frequency of insurance claims. There is a vast literature focused on the univariate case of zero-inflated count models, while work in the area of multivariate models is considerably less advanced. Given that insurance companies write multiple lines of insurance business, where the claim counts on these lines of business are often correlated, there is a strong incentive to analyze multivariate claim count models. Motivated by the idea of Liu and Tian (Computational Statistics and Data Analysis, 83, 200–222; 2015), we develop a multivariate zero-inflated hurdle model to describe multivariate count data with extra zeros. This generalization offers more flexibility in modeling the behavior of individual claim counts while also incorporating a correlation structure between claim counts for different lines of insurance business. We develop an application of the expectation–maximization (EM) algorithm to enable the statistical inference necessary to estimate the parameters associated with our model. Our model is then applied to an automobile insurance portfolio from a major insurance company in Spain. We demonstrate that the model performance for the multivariate zero-inflated hurdle model is superior when compared to several alternatives.

Effects of knowledge spillovers between competitors on patent quality: what patent citations reveal about a global duopoly

This paper analyses the effects on patent quality of a type of spillovers arising from the disclosure of patent information by firms engaged in competition in a global duopoly. Both firms are involved in producing new technologies and they do not cooperate on joint patents. In this context, we explored whether the disclosure of crucial knowledge in the patents of one of the firms affects the patent quality of its respective competitor. The empirical methodology relies on forward citations as an indicator of quality, and backward citations to the competitor as a measure of spillovers. We estimated several count models with a sample of 7750 patent families (divided into subsamples) owned by two large companies, Airbus and Boeing. Our econometric findings show that, for technologies in which the two firms account for the majority of the global patents, neither of the firms in the duopoly was able to harness spillovers from the rival to improve the quality of its patents. However, knowledge from the competitor becomes relevant, at least for one of the focal firms, in explaining patent quality of other technologies in which the two firms do not exert a dominant position.

Modelling Claim Frequency in Insurance Using Count Models

Background: In modelling claim frequency in actuary science, a major challenge is the number of zero claims associated with datasets. Aim: This study compares six count regression models on motorcycle insurance data. Methodology: The Akaike Information Criteria (AIC) and the Bayesian Information Criterion (BIC) were used for selecting best models. Results: Result of analysis showed that the Zero-Inflated Poisson (ZIP) with no regressors for the zero component gives the best predictive ability for the data with the least BIC while the classical Negative Binomial model gives the best result for explanatory purpose with the least AIC.

The risk factors of under-five deaths in rural parts of Ethiopia

Background of the study: Under-five mortality is the likelihood for a child born alive to die between birth and fifth birth day. Mortality under the age of five has been the main problem in public health policies especially in rural parts of Ethiopia.Objective: The objective of this study was to assess the risk factors of under-five mortality in Ethiopia using the 2011 EDHS data. Results: Information from 8,668 women included in the study show that 64.5% of the women never experienced under-five deaths of their children. Among four possible count models considered, the ZINB regression model was selected as the most appropriate model. Conclusion: The study revealed that mother’s age first birth, breastfeeding status, wealth index, whether the mother is currently working, region and mother’s level of education had statistically significant association with the number of under-five deaths in rural parts of Ethiopia.

Assessing the risk factors of under-five deaths in rural parts of Ethiopia

Background of the study: Under-five mortality is the likelihood for a child born alive to die between birth and fifth birth day. Mortality under the age of five has been the main problem in public health policies especially in rural parts of Ethiopia.Objective: The objective of this study was to assess the risk factors of under-five mortality in Ethiopia using the 2011 EDHS data. Results: Information from 8,668 women included in the study show that 64.5% of the women never experienced under-five deaths of their children. Among four possible count models considered, the ZINB regression model was selected as the most appropriate model. Conclusion: The study revealed that mother’s age first birth, breastfeeding status, wealth index, whether the mother is currently working, region and mother’s level of education had statistically significant association with the number of under-five deaths in rural parts of Ethiopia.

A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models

It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data