# zbMATH — the first resource for mathematics

Generalised linear models for aggregate claims: to Tweedie or not? (English) Zbl 1329.91075
Summary: The compound Poisson distribution with gamm a claim sizes is a very common model for premium estimation in Property and Casualty insurance. Under this distributional assumption, generalised linear models (GLMs) are used to estimate the mean claim frequency and severity, then these estimators are simply multiplied to estimate the mean aggregate loss. The Tweedie distribution allows to parametrise the compound Poisson-gamma (CPG) distribution as a member of the exponential dispersion family and then fit a GLM with a CPG distribution for the response. Thus, with the Tweedie distribution it is possible to estimate the mean aggregate loss using GLMs directly, without the need to previously estimate the mean frequency and severity separately. The purpose of this educational note is to explore the differences between these two estimation methods, contrasting the advantages and disadvantages of each.

##### MSC:
 91B30 Risk theory, insurance (MSC2010) 62J12 Generalized linear models (logistic models) 62P05 Applications of statistics to actuarial sciences and financial mathematics
##### Keywords:
Tweedie distribution; GLMs; exponential dispersion family
##### Software:
CASdatasets; Tweedie
Full Text:
##### References:
 [1] Bailey, RA; Simon, L, Two studies in automobile insurance ratemaking, ASTIN Bull, 1, 192-217, (1960) [2] Briere-Giroux G, Huet J-F, Spaul R, Staudt A, Weinsier D (2010) Predictive modeling for life insurers. https://www.soa.org/files/pdf/research-pred-mod-life-huet.pdf · Zbl 1094.91514 [3] Czado, C; Kastenmeier, R; Brechmann, EC; Min, A, A mixed copula model for insurance claims and claim sizes, Scand Actuarial J, 4, 278-305, (2012) · Zbl 1277.62249 [4] Dunn PK (2014) Tweedie: Tweedie exponential family models. R package. Version 2.2.1 · Zbl 1290.91092 [5] Dutang C (2015) Standard statistical inference. In: Charpentier A (eds) Computational actuarial science with R. CRC Press, New York, pp 75-125 · Zbl 1290.91092 [6] Gilchrist R, Drinkwater D (1999) Fitting Tweedie models to data with probability of zero responses. In: Friedl H, Berghold A, Kauermann G (eds) Proceedings of the 14th international workshop on statistical modelling. Statistical Modelling Society, Hong Kong, pp 207-214 [7] Jørgensen B (1992) The theory of exponential dispersion models and analysis of deviance. Instituto de Matemática Pura e Aplicada, (IMPA), Brazil · Zbl 0983.62502 [8] Jørgensen B (1997) The theory of dispersion models. Chapman & Hall, London · Zbl 1277.62249 [9] Jørgensen B, Paes de Souza MC (1994) Fitting Tweedie’s compound Poisson model to insurance claims data. Scand Actuarial J (1):69-93 · Zbl 0802.62089 [10] Krämer, N; Brechmann, EC; Silvestrini, D; Czado, C, Total loss estimation using copula-based regression models, Insur Math Econ, 53, 829-839, (2013) · Zbl 1290.91092 [11] Ohlsson E, Johansson B (2010) Non-life insurance princing with generalized linear models. Springer, Berlin · Zbl 1194.91011 [12] Smyth, GK; Jørgensen, B, Fitting tweedie’s compound Poisson model to insurance claims data: dispersion modelling, ASTIN Bull, 32, 143-157, (2002) · Zbl 1094.91514 [13] Smyth, GK; Verbyla, AP, Adjusted likelihood methods for modelling dispersion in generalized linear models, Environmetrics, 10, 695-709, (1999) [14] Song, P, Multivariate dispersion models generated from Gaussian copula, Scand J Stat, 27, 305-320, (2000) · Zbl 0955.62054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.