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In risk analysis, a global fit that appropriately captures the body and thetail of the distribution of losses is essential. Modelling the whole range ofthe losses using a standard distribution is usually very hard and oftenimpossible due to the specific characteristics of the body and the tail of theloss distribution. A possible solution is to combine two distributions in asplicing model: a light-tailed distribution for the body which covers light andmoderate losses, and a heavy-tailed distribution for the tail to capture largelosses. We propose a splicing model with a mixed Erlang (ME) distribution forthe body and a Pareto distribution for the tail. This combines the flexibilityof the ME distribution with the ability of the Pareto distribution to modelextreme values. We extend our splicing approach for censored and/or truncateddata. Relevant examples of such data can be found in financial risk analysis.We illustrate the flexibility of this splicing model using practical examplesfrom risk measurement.

Modelling Censored Losses Using Splicing: a Global Fit Strategy With Mixed Erlang and Extreme Value Distributions