An application of Zero-One Inflated Beta regression models for predicting health insurance reimbursement

零膨胀Tweedie模型中的离散建模及其在保险索赔数据分析中的应用

Dispersion Modeling in Zero-inflated Tweedie Models with Applications to Insurance Claim Data Analysis

针对保险索赔数据中零膨胀导致的Tweedie模型性能下降问题，本文提出在零膨胀Tweedie模型中同时建模均值、离散参数和零状态概率，并采用基于决策树的梯度提升方法，数值实验验证了其优越性。

Tweedie Gradient Boosting for Extremely Unbalanced Zero-inflated Data

Tweedie's compound Poisson model is a popular method to model insurance claims with probability mass at zero and nonnegative, highly right-skewed distribution. In particular, it is not uncommon to have extremely unbalanced data with excessively large proportion of zero claims, and even traditional Tweedie model may not be satisfactory for fitting the data. In this paper, we propose a boosting-assisted zero-inflated Tweedie model, called EMTboost, that allows zero probability mass to exceed a traditional model. We makes a nonparametric assumption on its Tweedie model component, that unlike a li…

Modeling Frequency and Severity of Claims with the Zero-Inflated Generalized Cluster-Weighted Models

In this paper, we propose two important extensions to cluster-weighted models (CWMs). First, we extend CWMs to have generalized cluster-weighted models (GCWMs) by allowing modeling of non-Gaussian distribution of the continuous covariates, as they frequently occur in insurance practice. Secondly, we introduce a zero-inflated extension of GCWM (ZI-GCWM) for modeling insurance claims data with excess zeros coming from heterogenous sources. Additionally, we give two expectation-optimization (EM) algorithms for parameter estimation given the proposed models. An appropriate simulation study shows t…

A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate--Making Systems

This article introduces a k-Inflated Negative Binomial mixture distribution/regression model as a more flexible alternative to zero-inflated Poisson distribution/regression model. An EM algorithm has been employed to estimate the model's parameters. Then, such new model along with a Pareto mixture model have been employed to design an optimal rate--making system. Namely, this article employs number/size of reported claims of Iranian third party insurance dataset. Then, it employs the k-Inflated Negative Binomial mixture distribution/regression model as well as other well developed counting mod…

A Pareto scale-inflated outlier model and its Bayesian analysis

This paper develops a Pareto scale-inflated outlier model. This model is intended for use when data from some standard Pareto distribution of interest is suspected to have been contaminated with a relatively small number of outliers from a Pareto distribution with the same shape parameter but with an inflated scale parameter. The Bayesian analysis of this Pareto scale-inflated outlier model is considered and its implementation using the Gibbs sampler is discussed. The paper contains three worked illustrative examples, two of which feature actual insurance claims data.

零膨胀数据的基于秩的一致性：新表示、估计量与精确界

Rank-based concordance for zero-inflated data: New representations, estimators, and sharp bounds

针对零膨胀连续数据中结导致传统秩一致性估计失效的问题，本文重构 Gini's gamma 与 Spearman's footrule、修正 Spearman's rho，并给出精确上下界及模拟和实际应用验证。