Abstract
This paper will discuss the modeling claim severity of ThirdParty Liability insurance using a mixed Rayleigh-Rayleigh distribution. The mixed Rayleigh-Rayleigh distribution is a distribution built on the basis of an infinitely mixed distribution. The mixed Rayleigh-Rayleigh distribution is a continuous distribution with one parameter, namely α. Parameters in the mixed Rayleigh-Rayleigh distribution can be estimated using the maximum likelihood estimator method through the Newton-Raphson iteration numerical method. The distribution fit test was carried out using the Kolmogorov-Smirnov fit test. The data used is data on Third Party Liability insurance claims with comprehensive coverage at PT. X for the 2019 policy for category 2 in all regions. Based on the results of applying the mixed Rayleigh-Rayleigh distribution on the data claim severity of Third Party Liability insurance with comprehensive coverage at PT. X in 2019 category 2 using the Kolmogorov-Smirnov test it can be concluded that the claims severity in regions 1 and 3 come from populations with a mixed Rayleigh-Rayleigh distribution, while the claim severity claims in region 2 come from populations that don't have a mixed Rayleigh-Rayleigh distribution.
 
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