By Piet de Jong, Gillian Z. Heller
This is often the single ebook actuaries have to comprehend generalized linear versions (GLMs) for assurance functions. GLMs are utilized in the assurance to help severe judgements. formerly, no textual content has brought GLMs during this context or addressed the issues particular to assurance facts.
Using assurance facts units, this functional, rigorous publication treats GLMs, covers all usual exponential relatives distributions, extends the technique to correlated facts buildings, and discusses fresh advancements which transcend the GLM. the problems within the e-book are particular to assurance facts, similar to version choice within the presence of enormous facts units and the dealing with of various publicity instances.
Exercises and data-based practicals aid readers to consolidate their abilities, with options and information units given at the better half web site. even if the booklet is package-independent, SAS code and output examples function in an appendix and at the web site. furthermore, R code and output for all of the examples are supplied at the web site.
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Extra resources for Generalized Linear Models for Insurance Data (International Series on Actuarial Science)
9. 9 policies on which there were no claims. Numerous risk factors are given. This data set is used in exercises. 9 Outline of rest of book Chapters 2–4 provide the necessary statistical background for the development of the GLM. Chapter 2 covers the response distributions encountered in generalized linear modeling, and Chapter 3 covers the exponential family of distributions and maximum likelihood estimation. Chapter 4 provides an introduction to the classical normal linear model. Regression concepts which carry across to the GLM, such as collinearity and interaction, are covered in this chapter.
A regression analysis with claim size as the response, and driver’s age and sex as explanatory variables, is appropriate. This may be carried out in two ways: (i) the “grouped data” approach. 1, with regression weights equal to the number of observations in each cell; (ii) the “ungrouped data” approach. This is based on the 4624 raw observations. The two approaches yield the same parameter estimates. The grouped data approach has been, and still is, popular, as data representation and storage is dramatically simpler in cases such as the current example.
To make this dependence explicit write the probability function as f (yi ; θ, φ). If the yi are independent then their joint probability function is n f (yi ; θ, φ) . f (y; θ, φ) = i=1 The likelihood of the sample (y1 , . . , yn ) is the above expression regarded as a function of θ and φ. The log-likelihood (θ, φ) is the logarithm of the likelihood: n (θ, φ) ≡ ln f (yi ; θ, φ) . i=1 40 Exponential family responses and estimation The method of maximum likelihood chooses those values of θ and φ which maximize the likelihood or equivalently, the log-likelihood.
Generalized Linear Models for Insurance Data (International Series on Actuarial Science) by Piet de Jong, Gillian Z. Heller