Economics - Research Publications

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    Likelihood Based Inference and Bias Reduction in the Modified Skew-t-Normal Distribution
    Arrue, J ; Arellano-Valle, RB ; Calderin-Ojeda, E ; Venegas, O ; Gomez, HW (MDPI, 2023-08)
    In this paper, likelihood-based inference and bias correction based on Firth’s approach are developed in the modified skew-t-normal (MStN) distribution. The latter model exhibits a greater flexibility than the modified skew-normal (MSN) distribution since it is able to model heavily skewed data and thick tails. In addition, the tails are controlled by the shape parameter and the degrees of freedom. We provide the density of this new distribution and present some of its more important properties including a general expression for the moments. The Fisher’s information matrix together with the observed matrix associated with the log-likelihood are also given. Furthermore, the non-singularity of the Fisher’s information matrix for the MStN model is demonstrated when the shape parameter is zero. As the MStN model presents an inferential problem in the shape parameter, Firth’s method for bias reduction was applied for the scalar case and for the location and scale case.
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    Asymmetric versus Symmetric Binary Regresion: A New Proposal with Applications
    Gomez-Deniz, E ; Calderin-Ojeda, E ; Gomez, HW (MDPI, 2022-04)
    The classical logit and probit models allow to explain a dichotomous dependent variable as a function of factors or covariates which can influence the response variable. This paper introduces a new skew-logit link for item response theory by considering the arctan transformation over the scobit logit model, yielding a very flexible link function from a new class of generalized distribution. This approach assumes an asymmetric model, which reduces to the standard logit model for a special case of the parameters that control the distribution’s symmetry. The model proposed is simple and allows us to estimate the parameters without using Bayesian methods, which requires implementing Markov Chain Monte Carlo methods. Furthermore, no special function appears in the formulation of the model. We compared the proposed model with the classical logit specification using three datasets. The first one deals with the well-known data collection widely studied in the statistical literature, concerning with mortality of adult beetle after exposure to gaseous carbon disulphide, the second one considers an automobile insurance portfolio. Finally, the third dataset examines touristic data related to tourist expenditure. For these examples, the results illustrate that the new model changes the significance level of some explanatory variables and the marginal effects. For the latter example, we have also modified the definition of the intercept in the linear predictor to prevent confounding.
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    A Copula Type-Model for Examining the Role of Microbiome as a Potential Tool in Diagnosis
    Calderin-Ojeda, E ; Lopez-Campos, G ; Gomez-Deniz, E ; Li, X (HINDAWI LTD, 2022-06-06)
    Continuous advancements in biotechnology are generating new knowledge and data sources that might be of interest for the insurance industry. A paradigmatic example of these advancements is genetic information which can reliably notify about future appearance of certain diseases making it an element of great interest for insurers. However, this information is considered by regulators in the highest confidentiality level and protected from disclosure. Recent investigations have shown that the microbiome can be correlated with several health conditions. In this paper, we examine the potential use of microbiome information as a potential tool for cardiovascular diagnosis. By using a recent dataset, we analyze the relation of some variables associated to coronary illnesses and several components of the microbiome in the organism by using a new copula-based multivariate regression model for compositional data in the predictor. Our findings show that the coabundance group associated to Ruminococcaceae-Bifidobacteriaceae has a negative impact on the age for nonsedentary individuals. However, one should be cautious with this conclusion since environmental conditions also influence the baseline microbiome.
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    A Compound Class of the Inverse Gamma and Power Series Distributions
    Rivera, PA ; Calderin-Ojeda, E ; Gallardo, DI ; Gomez, HW (MDPI, 2021-08-01)
    In this paper, the inverse gamma power series (IGPS) class of distributions asymmetric is introduced. This family is obtained by compounding inverse gamma and power series distributions. We present the density, survival and hazard functions, moments and the order statistics of the IGPS. Estimation is first discussed by means of the quantile method. Then, an EM algorithm is implemented to compute the maximum likelihood estimates of the parameters. Moreover, a simulation study is carried out to examine the effectiveness of these estimates. Finally, the performance of the new class is analyzed by means of two asymmetric real data sets.
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    A Priori Ratemaking Selection Using Multivariate Regression Models Allowing Different Coverages in Auto Insurance
    Gomez-Deniz, E ; Calderin-Ojeda, E (MDPI AG, 2021-07-01)
    A comprehensive auto insurance policy usually provides the broadest protection for the most common events for which the policyholder would file a claim. On the other hand, some insurers offer extended third-party car insurance to adapt to the personal needs of every policyholder. The extra coverage includes cover against fire, natural hazards, theft, windscreen repair, and legal expenses, among some other coverages that apply to specific events that may cause damage to the insured’s vehicle. In this paper, a multivariate distribution, based on a conditional specification, is proposed to account for different numbers of claims for different coverages. Then, the premium is computed for each type of coverage separately rather than for the total claims number. Closed-form expressions are given for moments and cross-moments, parameter estimates, and for a priori premiums when different premiums principles are considered. In addition, the severity of claims can be incorporated into this multivariate model to derive multivariate claims’ severity distributions. The model is extended by developing a zero-inflated version. Regression models for both multivariate families are derived. These models are used to fit a real auto insurance portfolio that includes five types of coverage. Our findings show that some specific covariates are statistically significant in some coverages, yet they are not so for others.
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    Financial and Actuarial Properties of the Beta-Pareto as a Long-Tail Distribution
    Gómez-Déniz, E ; Calderín-Ojeda, E (INE-Instituto Nacional de Estadistica de Espana, 2021-01-01)
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    A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory
    Reyes, J ; Gomez-Deniz, E ; Gomez, HW ; Calderin-Ojeda, E (MDPI, 2021-04-01)
    There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.
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    A Survey of the Individual Claim Size and Other Risk Factors Using Credibility Bonus-Malus Premiums
    Gomez-Deniz, E ; Calderin-Ojeda, E (MDPI AG, 2020-02-01)
    In this paper, a flexible count regression model based on a bivariate compound Poisson distribution is introduced in order to distinguish between different types of claims according to the claim size. Furthermore, it allows us to analyse the factors that affect the number of claims above and below a given claim size threshold in an automobile insurance portfolio. Relevant properties of this model are given. Next, a mixed regression model is derived to compute credibility bonus-malus premiums based on the individual claim size and other risk factors such as gender, type of vehicle, driving area, or age of the vehicle. Results are illustrated by using a well-known automobile insurance portfolio dataset.
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    Modeling the Conditional Dependence between Discrete and Continuous Random Variables with Applications in Insurance
    Gomez-Deniz, E ; Calderin-Ojeda, E (MDPI, 2021-01-01)
    We jointly model amount of expenditure for outpatient visits and number of outpatient visits by considering both dependence and simultaneity by proposing a bivariate structural model that describes both variables, specified in terms of their conditional distributions. For that reason, we assume that the conditional expectation of expenditure for outpatient visits with respect to the number of outpatient visits and also, the number of outpatient visits expectation with respect to the expenditure for outpatient visits is related by taking a linear relationship for these conditional expectations. Furthermore, one of the conditional distributions obtained in our study is used to derive Bayesian premiums which take into account both the number of claims and the size of the correspondent claims. Our proposal is illustrated with a numerical example based on data of health care use taken from Medical Expenditure Panel Survey (MEPS), conducted by the U.S. Agency of Health Research and Quality.
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    On the Type I multivariate zero-truncated hurdle model with applications in health insurance
    Zhang, P ; Calderin, E ; Li, S ; Wu, X (Elsevier, 2020-01-01)
    In the general insurance modeling literature, there has been a lot of work based on univariate zero-truncated models, but little has been done in the multivariate zero-truncation cases, for instance a line of insurance business with various classes of policies. There are three types of zero-truncation in the multivariate setting: only records with all zeros are missing, zero counts for one or some classes are missing, or zeros are completely missing for all classes. In this paper, we focus on the first case, the so-called Type I zero-truncation, and a new multivariate zero-truncated hurdle model is developed to study it. The key idea of developing such a model is to identify a stochastic representation for the underlying random variables, which enables us to use the EM algorithm to simplify the estimation procedure. This model is used to analyze a health insurance claims dataset that contains claim counts from different categories of claims without common zero observations.