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Statistical Analysis and Modeling of Claim Duration for Workers' Compensation Insurance
Mathematics and Statistics
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Workers' compensation is a form of insurance that protects employees and business owners from the cost of injuries occurring in the workplace. The duration of time a workers' compensation claim remains open largely depends on the type and severity of the injury. This work focuses on statistical analysis and modeling of claim duration for a workers' compensation insurer. A data set for claim duration that included over two million claims spanning from 1915 to 1994 was analyzed. Exploratory data analysis revealed that the distribution of the data was multi-modal with a gap at approximately 55 years and a positive skew. Log linear analysis and modeling was used to understand the association between categorical variables. The EM algorithm was used to fit gamma and normal mixture models to the claim duration data. Log likelihood and AIC values were used to show that a normal mixture provided the best fit for the data. The likelihood ratio test was used to select the number of components in the mixture model. This test indicated the four component normal mixture model was the best model. The Komogorov-Smirnov goodness-of-fit test indicated that the selected model was identical to the population distribution that generated the data. Finally, standard errors of the parameter estimates were reported indicating that little uncertainty existed in the estimates.