LEADER 05367nam 2200625 a 450 001 9910143586103321 005 20210914172720.0 010 $a1-280-97406-0 010 $a9786610974061 010 $a0-470-51742-5 010 $a0-470-51741-7 035 $a(CKB)1000000000357139 035 $a(EBL)315071 035 $a(OCoLC)476106132 035 $a(SSID)ssj0000096988 035 $a(PQKBManifestationID)11126391 035 $a(PQKBTitleCode)TC0000096988 035 $a(PQKBWorkID)10113627 035 $a(PQKB)10412079 035 $a(MiAaPQ)EBC315071 035 $a(EXLCZ)991000000000357139 100 $a20070517d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aActuarial modelling of claim counts$b[electronic resource] $erisk classification, credibility and bonus-malus systems /$fMichel Denuit ... [et al.] 210 $aChichester, West Sussex, England ;$aHoboken, NJ $cWiley$dc2007 215 $a1 online resource (386 p.) 300 $aDescription based upon print version of record. 311 $a0-470-02677-4 320 $aIncludes bibliographical references (p. [345]-353) and index. 327 $aActuarial Modelling of Claim Counts; Contents; Foreword; Preface; Notation; Part I Modelling Claim Counts; 1 Mixed Poisson Models for Claim Numbers; 1.1 Introduction; 1.1.1 Poisson Modelling for the Number of Claims; 1.1.2 Heterogeneity and Mixed Poisson Model; 1.1.3 Maximum Likelihood Estimation; 1.1.4 Agenda; 1.2 Probabilistic Tools; 1.2.1 Experiment and Universe; 1.2.2 Random Events; 1.2.3 Sigma-Algebra; 1.2.4 Probability Measure; 1.2.5 Independent Events; 1.2.6 Conditional Probability; 1.2.7 Random Variables and Random Vectors; 1.2.8 Distribution Functions 327 $a1.2.9 Independence for Random Variables1.3 Poisson Distribution; 1.3.1 Counting Random Variables; 1.3.2 Probability Mass Function; 1.3.3 Moments; 1.3.4 Probability Generating Function; 1.3.5 Convolution Product; 1.3.6 From the Binomial to the Poisson Distribution; 1.3.7 Poisson Process; 1.4 Mixed Poisson Distributions; 1.4.1 Expectations of General Random Variables; 1.4.2 Heterogeneity and Mixture Models; 1.4.3 Mixed Poisson Process; 1.4.4 Properties of Mixed Poisson Distributions; 1.4.5 Negative Binomial Distribution; 1.4.6 Poisson-Inverse Gaussian Distribution 327 $a1.4.7 Poisson-LogNormal Distribution1.5 Statistical Inference for Discrete Distributions; 1.5.1 Maximum Likelihood Estimators; 1.5.2 Properties of the Maximum Likelihood Estimators; 1.5.3 Computing the Maximum Likelihood Estimators with the Newton-Raphson Algorithm; 1.5.4 Hypothesis Tests; 1.6 Numerical Illustration; 1.7 Further Reading and Bibliographic Notes; 1.7.1 Mixed Poisson Distributions; 1.7.2 Survey of Empirical Studies Devoted to Claim Frequencies; 1.7.3 Semiparametric Approach; 2 Risk Classification; 2.1 Introduction; 2.1.1 Risk Classification, Regression Models and Random Effects 327 $a2.1.2 Risk Sharing in Segmented Tariffs2.1.3 Bonus Hunger and Censoring; 2.1.4 Agenda; 2.2 Descriptive Statistics for Portfolio A; 2.2.1 Global Figures; 2.2.2 Available Information; 2.2.3 Exposure-to-Risk; 2.2.4 One-Way Analyses; 2.2.5 Interactions; 2.2.6 True Versus Apparent Dependence; 2.3 Poisson Regression Model; 2.3.1 Coding Explanatory Variables; 2.3.2 Loglinear Poisson Regression Model; 2.3.3 Score; 2.3.4 Multiplicative Tariff; 2.3.5 Likelihood Equations; 2.3.6 Interpretation of the Likelihood Equations; 2.3.7 Solving the Likelihood Equations with the Newton-Raphson Algorithm 327 $a2.3.8 Wald Confidence Intervals2.3.9 Testing for Hypothesis on a Single Parameter; 2.3.10 Confidence Interval for the Expected Annual Claim Frequency; 2.3.11 Deviance; 2.3.12 Deviance Residuals; 2.3.13 Testing a Hypothesis on a Set of Parameters; 2.3.14 Specification Error and Robust Inference; 2.3.15 Numerical Illustration; 2.4 Overdispersion; 2.4.1 Explanation of the Phenomenon; 2.4.2 Interpreting Overdispersion; 2.4.3 Consequences of Overdispersion; 2.4.4 Modelling Overdispersion; 2.4.5 Detecting Overdispersion; 2.4.6 Testing for Overdispersion; 2.5 Negative Binomial Regression Model 327 $a2.5.1 Likelihood Equations 330 $aThere are a wide range of variables for actuaries to consider when calculating a motorist's insurance premium, such as age, gender and type of vehicle. Further to these factors, motorists' rates are subject to experience rating systems, including credibility mechanisms and Bonus Malus systems (BMSs). Actuarial Modelling of Claim Counts presents a comprehensive treatment of the various experience rating systems and their relationships with risk classification. The authors summarize the most recent developments in the field, presenting ratemaking systems, whilst taking into account e 606 $aAutomobile insurance$xRates$zEurope 606 $aAutomobile insurance claims$zEurope 608 $aElectronic books. 615 0$aAutomobile insurance$xRates 615 0$aAutomobile insurance claims 676 $a368.092 676 $a368.092094 701 $aDenuit$b M$g(Michel)$0781288 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143586103321 996 $aActuarial modelling of claim counts$92052432 997 $aUNINA