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Exponential Dispersion (ED) Distributions

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Effective Statistical Learning Methods for Actuaries I

Part of the book series: Springer Actuarial ((SPACLN))

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Abstract

This chapter is devoted to the study of the family of Exponential Dispersion (or ED) distributions that are central to insurance data analytics techniques. 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 according to the format of the response. Particular attention is paid to the effect of averaging and weighting with ED distributions.

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Notes

  1. 1.

    In this book, we assume that all moments of the random variables under consideration exist and are finite when they are written (except in the Log-Gamma, or Pareto case, this is always the case with distributions discussed here).

  2. 2.

    Sometimes, the Pascal distribution is called the Negative Binomial one, where “negative” refers to the counted failures. In this book, we reserve this name for the general case where the parameter m is allowed to assume positive, non-integer values. This extension will be discussed in Chap. 5.

References

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  • Klugman SA, Panjer HH, Willmot GE (2012) Loss models: from data to decisions, 4th edn. Wiley

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Correspondence to Michel Denuit .

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Denuit, M., Hainaut, D., Trufin, J. (2019). Exponential Dispersion (ED) Distributions. In: Effective Statistical Learning Methods for Actuaries I. Springer Actuarial(). Springer, Cham. https://doi.org/10.1007/978-3-030-25820-7_2

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