58,759 research outputs found
A priori ratemaking using bivariate poisson regression models
No full textIn automobile insurance, it is useful to achieve a priori ratemaking by resorting to generalized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper examines an a priori ratemaking procedure when including two di®erent types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tariff system might be affected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.
A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts
No full textIn this paper a purely theoretical reinsurance model is presented, where the reinsurance contract is assumed to be simultaneously of an excess-of-loss and of a proportional type. The stochastic structure of the set of pairs (claim’s arrival time, claim’s size) is described by a Spatial Mixed Poisson Process. By using an invariance property of the Spatial Mixed Poisson Processes, we estimate the amount that the ceding company obtains in a fixed time interval in force of the reinsurance contract
Modelling dependence in a ratemaking procedure with multivariate Poisson regression models
No full textWhen actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce di®erent multivariate Poisson regression models in order to relax the independence assumption, including zero-in°ated models to account for excess of zeros and overdispersion. These models have been largely ignored to date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.Multivariate Poisson regression models, Zero-inflated models, Automobile insurance, MCMC inference, Gibbs sampling
Congestion probabilities in CDMA-based networks supporting batched Poisson traffic
No full textWe propose a new multirate teletraffic loss model for the calculation of time and call\ud
congestion probabilities in CDMA-based networks that accommodate calls of different serviceclasses\ud
whose arrival follows a batched Poisson process. The latter is more “peaked” and\ud
“bursty” than the ordinary Poisson process. The acceptance of calls in the system is based on the\ud
partial batch blocking discipline. This policy accepts a part of the batch (one or more calls) and\ud
discards the rest if the available resources are not enough to accept the whole batch. The\ud
proposed model takes into account the multiple access interference, the notion of local (soft)\ud
blocking, user’s activity and the interference cancellation. Although the analysis of the model\ud
does not lead to a product form solution of the steady state probabilities, we show that the\ud
calculation of the call-level performance metrics, time and call congestion probabilities, can be\ud
based on approximate but recursive formulas. The accuracy of the proposed formulas are\ud
verified through simulation and found to be quite satisfactory
Robust designs for poisson regression models
No full textWe consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates.Given certain constraints in themethodology, itmay be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs that perform similarly, in terms of estimation, to current techniques and offers the solution in a more timely manner.We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative
On the Existence of the Maximum Likelihood Estimates for Poisson Regression
No full textWe note that the existence of the maximum likelihood estimates for Poisson regression depends on the data configuration. Because standard software does not check for this problem, the practitioner may be surprised to find that in some applications estimation of the Poisson regression is unusually difficult or even impossible. More seriously, the estimation algorithm may lead to spurious maximum likelihood estimates. We identify the signs of the non-existence of the maximum likelihood estimates and propose a simple empirical strategy to single out the regressors causing this type of identification failure.Poisson estimation, gravity equation
Variations on the Author
No full text“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
HURDLE COUNT-DATA MODELS IN RECREATION DEMAND ANALYSIS
No full textWhen a sample of recreators is drawn from the general population using a survey, many in the sample will not recreate at a recreation site of interest. This study focuses on nonparticipation in recreation demand modeling and the use of modified count-data models. We clarify the meaning of the single-hurdle Poisson (SHP) model and derive the double-hurdle Poisson (DHP) model. The latter is contrasted with the SHP and we show the DHP is consistent with Johnson and Kotz's zero-modified Poisson model.Resource /Energy Economics and Policy,
BAYESIAN ANALYSIS OF THE COMPOUND COLLECTIVE MODEL: THE NET PREMIUM PRINCIPLE WITH EXPONENTIAL POISSON AND GAMMA–GAMMA DISTRIBUTIONS
No full textThis article develops a Bayesian analysis of the Compound Collective Model utilizing the Net Premium Principle, considering single-period models. With respect to likelihoods, we used a Poisson distribution for the number of claims and an Exponential distribution for the severity of the accident/event. Gamma distributions were used for the prior distributions. The robustness of the posterior premium was analyzed with respect to the prior distribution specification of the severity of the accident/event, utilizing contamination classes, these being the class of all the distributions and that of all the unimodal distributions with the same mode. Numerical applications of the results obtained were performed.Compound collective model; Bayesian analysis; Robustness analysis.
The road from London to Chichester in com, Suffex : containing 63 mile 2 furlongs vizt. : from ye standard in Cornhill London to Guilford in com Surry ...
No full textRelief shown pictorially.; Road strip map in six sections, with numbered distances along road.; Orientation of north shown in each section..; Derived from John Ogilby's Britannia.; 39 in lower right corner.; Decorative cartouche around title statement
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