This paper presents an extension of #statistical inference for smoothed quantile estimators from finite domains to infinite domains. A new truncation methodology is proposed for discrete loss distributions with infinite domains. #simulation studies using several distributions commonly used in the #insuranceindustry show the effectiveness of the methodology. The authors also propose a flexible bootstrap-based approach and demonstrate its use in computing the conditional five number summary (C5NS) for tail risk and constructing confidence intervals for each of the five quantiles that make up C5NS. Results using #automobile #accident #data show that the smoothed quantile approach produces more accurate classifications of tail #risk and lower coefficients of variation in the estimation of tail #probabilities compared to the linear interpolation approach.

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