Predictive Modeling Applications in Actuarial Science
 Volume 1
 Introduction
 Predictive Modeling Foundations
 Predictive Modeling Methods
 Bayesian and Mixed Modeling
 Longitudinal Modeling
 Volume 2
 Generalized Linear Model
 Extensions of the Generalized Linear Model
 Unsupervised Predictive Modeling Methods

Applications on Current Problems in Actuarial Science
 Chapter 8  The Predictive Distribution of Loss Reserve Estimates over a Finite Time Horizon
 Chapter 9  Finite Mixture Model and Workersâ€™ Compensation LargeLoss Regression Analysis
 Chapter 10  A Framework for Managing Claim Escalation Using Predictive Modeling
 Chapter 11  Predictive Modeling for UsageBased Auto Insurance
Chapter 9  Finite Mixture Model and Workersâ€™ Compensation LargeLoss Regression Analysis
Authors
Luyang Fu  Cincinnati Insurance Companies
luyang_fu@Yahoo.com
Xianfang Liu  Cincinnati Insurance Companies
Frank_Liu@cinfin.com
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Actuaries have been studying loss distributions since the emergence of the profession. Numerous studies have found that the widely used distributions, such as lognormal, Pareto, and gamma, do not fit insurance data well. Mixture distributions have gained popularity in recent years because of their flexibility in representing insurance losses from various sizes of claims, especially on the right tail. To incorporate the mixture distributions into the framework of popular generalized linear models (GLMs), the authors propose to use nite mixture models (FMMs) to analyze insurance loss data. The regression approach enhances the traditional wholebook distribution analysis by capturing the impact of individual explanatory variables. FMM improves the standard GLM by addressing distributionrelated problems, such as heteroskedasticity, over and underdispersion, unobserved heterogeneity, and fat tails. A case study with applications on claims triage and on highdeductible pricing using workersâ€™ compensation data illustrates those benefits.