In recent papers, Bonus-Malus Scales (BMS) estimated using data have been considered as an alternative to longitudinal data and hierarchical data approaches to model the dependence between different contracts for the same insured. Those papers, however, did not discuss in detail how to construct and understand BMS models, and many of the BMS’s basic properties were not discussed. The first objective of this paper is to correct this situation by explaining the logic behind BMS models and by describing those properties. More particularly, we will explain how BMS models are linked with simple count regression models that have covariates associated with the past claims experience. This study could help actuaries to understand how and why they should use BMS models for experience rating. The second objective of this paper is to create artificial past claims history for each insured. This is done by combining recent panel data theory with BMS models. We show that this addition significantly improves the prediction capacity of the BMS and provides a temporary solution for insurers who do not have enough historical data. We apply the BMS model to real data from a major Canadian insurance company. Results are analysed deeply to identify specific aspects of the BMS model.

In this paper, I introduce a Bayesian model for detecting changepoints in a time series of overdispersed counts, such as contributions to candidates over the course of a campaign or counts of terrorist violence. To avoid having to specify the number of changepoint ex ante, this model incorporates a hierarchical Dirichlet process prior to estimate the number of changepoints as well as their location. This allows researchers to discover salient structural breaks and perform inference on the number of such breaks in a given time series. I demonstrate the usefulness of the model with applications to campaign contributions in the 2012 U.S. Republican presidential primary and incidences of global terrorism from 1970 to 2015.

Policy-critical, micro-level statistical data are often unavailable at the desired level of disaggregation. We present a Bayesian methodology for “downscaling” aggregated count data to the micro level, using an outside statistical sample. Our procedure combines numerical simulation with exact calculation of combinatorial probabilities. We motivate our approach with an application estimating the number of farms in a region, using count totals at higher levels of aggregation. In a simulation analysis over varying population sizes, we demonstrate both robustness to sampling variability and outperformance relative to maximum likelihood. Spatial considerations, implementation of “informative” priors, non-spatial classification problems, and best practices are discussed.

Direct marketing strategies increasingly have been recognized as a viable business option in U.S. agriculture as they allow producers to receive a better price by selling products directly to consumers. The objective of this study is twofold. Using a national survey, we first estimated a zero-inflated negative binomial model to identify factors affecting the total number of direct marketing strategies adopted by farmers. Then we estimated a quantile regression model to assess the impact of the intensity of adoption of direct marketing strategies on gross cash farm income. The results show that the intensity of adoption has no significant impact on gross cash farm income and that participation in farmers markets is negatively correlated with gross cash farm income at all five quantiles estimated.

County agents receive cost of production information primarily from state extension services and then disseminate it to agricultural producers. A survey gathered data on agent usage of this information. A Poisson regression analysis using count data was performed to determine the factors influencing the number of times county agents directly referred to published cost of production (enterprise budget) information in a year. The agent's understanding of budget information use in management decisions, the availability of budgets, and his/her receiving the budgets in multiple forms (e.g., sheets, booklets, or software) had significant positive impacts on the use of budgets by the agent.

The number of insecticide applications made by an apple grower to control an insect infestation is modeled as a geometric random variable. Insecticide efficacy, rate per application, month of treatment, and method of application all have significant impacts on the expected number of applications. The number of applications to control a given insect population is dependent on the probability of achieving successful control with a given application. Results suggest that northeastern growers have the highest and mid-Atlantic growers the lowest probability of controlling an infestation with a given application. Results also indicate that scales require the least and moths the most number of applications. Growers are not responsive to per unit insecticide prices, but respond negatively to insecticide toxicity, supporting findings from previous pesticide demand analyses.

This study examines per trip consumer surplus associated with guided Whitewater rafting on two southern rivers. First, household recreation demand functions are estimated based on the individual travel cost model using truncated count data regression methods and alternative price specifications. Findings show mean per trip consumer surplus point estimates between $89 and $286, depending on modeling assumptions and river quality. Magnitudes of these surpluses are very dependent on assumptions about the opportunity cost of time.

We study the demand by organic farmers for technical advice using a quantile regression for the demand of organic farmers for consultations with private information providers. There is substantial heterogeneity in the impact of critical explanatory variables on consultations of organic farmer. Larger farm size has a positive effect on contacts, but the effect is absent for the highest number of consultations. Internet use has a positive marginal effect on visits to private information providers across each quantile, suggesting that expanded efforts to deliver programs through web-based resources are a useful investment for information providers.

Ratemaking is one of the most important tasks of non-life actuaries. Usually, the ratemaking process is done in two steps. In the first step, a priori ratemaking, an a priori premium is computed based on the characteristics of the insureds. In the second step, called the a posteriori ratemaking, the past claims experience of each insured is considered to the a priori premium and set the final net premium. In practice, for automobile insurance, this correction is usually done with bonus-malus systems, or variations on them, which offer many advantages. In recent years, insurers have accumulated longitudinal information on their policyholders, and actuaries can now use many years of informations for a single insured. For this kind of data, called panel or longitudinal data, we propose an alternative to the two-step ratemaking approach and argue this old approach should no longer be used. As opposed to a posteriori models of cross-section data, the models proposed in this paper generate premiums based on empirical results rather than inductive probability. We propose a new way to deal with bonus-malus systems when panel data are available. Using car insurance data, a numerical illustration using at-fault and non-at-fault claims of a Canadian insurance company is included to support this discussion. Even if we apply the model for car insurance, as long as another line of business uses past claim experience to set the premiums, we maintain that a similar approach to the model proposed should be used.

The authors review various facts about copulas linking discrete distributions. They show how the possibility of ties that results from atoms in the probability distribution invalidates various familiar relations that lie at the root of copula theory in the continuous case. They highlight some of the dangers and limitations of an undiscriminating transposition of modeling and inference practices from the continuous setting into the discrete one.

A unified way of obtaining stationary time series models with the univariate margins in the convolution-closed infinitely divisible class is presented. Special cases include gamma, inverse Gaussian, Poisson, negative binomial, and generalized Poisson margins. ARMA time series models obtain in the special case of normal margins, sometimes in a different stochastic representation. For the gamma and Poisson margins, some previously defined time series models are included, but for the negative binomial margin, the time series models are different and, in several ways, better than previously defined time series models. The models are related to multivariate distributions that extend a univariate distribution in the convolution-closed infinitely divisible class. Extensions to the non-stationary case and possible applications to modelling longitudinal data are mentioned.