Titlebook: Effective Statistical Learning Methods for Actuaries I; GLMs and Extensions Michel Denuit,Donatien Hainaut,Julien Trufin Textbook 2019 Spri

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暫時休息

Exponential Dispersion (ED) Distributionsques. The objective functions used to calibrate the regression models described in this book correspond to log-likelihoods taken from this family. This is why a good knowledge of these models is the necessary prerequisite to the next chapters, in order to understand which objective function to use a

憤怒事實

Maximum Likelihood Estimationors enjoy convenient theoretical properties, being optimal in a wide variety of situations. The maximum likelihood principle will be used throughout the next chapters to fit the supervised learning models.

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小卒

Over-Dispersion, Credibility Adjustments, Mixed Models, and Regularizationy results in correlation among the responses within the same group, casting doubts about the outputs of analyses assuming mutual independence. Random effects offer a convenient way to model such grouping structure. This chapter presents the Generalized Linear Mixed Model (GLMM) approach to regressio

易改變

Generalized Additive Models (GAMs)eatures coded by means of binary variables. However, this assumption becomes questionable for continuous features which may have a nonlinear effect on the score scale. This chapter is devoted to Generalized Additive Models (GAMs) which keep the additive decomposition of the score but allow the actua

易改變

Beyond Mean Modeling: Double GLMs and GAMs for Location, Scale and Shape (GAMLSS)ion, scale, shape or probability mass at the origin, for instance. This allows the actuary to let the available information enter other dimensions of the response, such as volatility or no-claim probability. The double GLM setting supplements GLMs with dispersion modeling, letting the dispersion par

有花

Some Generalized Non-linear Models (GNMs) to be learned from the data. GAMs can be fitted with the help of local versions of GLMs or by decomposing the nonlinear effects of the features in an appropriate spline basis so that the working scores are also linear functions of the regression parameters. In this chapter, models with a score invo

Ballad

Extreme Value Modelstions, with a particular emphasis on large claims in property and casualty insurance and mortality at oldest ages in life insurance. Large claims generally affect liability coverages and require a separate analysis. The reason for a separate analysis of small or moderate losses (also referred to as

排他

Over-Dispersion, Credibility Adjustments, Mixed Models, and Regularizationn analysis. In this framework, random effects are added on the same scale as the linear combination of the available features (called fixed effects). Predictive distributions, that is, conditional distribution of the response given past experience, are particularly attractive to re-valuate future premiums based on claims observed previously.