content_image/314988.jpg
The moments of f$_{i}$ ( · ; u ) are 

Introducing a non-zero lower bound is straightforward. 

## 6 NUMERICAL ILLUSTRATION 

<img src='content_image/314988.jpg'>

We have implemented the methods of this paper in a package for the R open source statistical computing environment (R Core Team, 2013), named tailloss . In addition, this package includes a large ELT for US hurricanes (32,060 rows). 

## 6.1 The effect of merging 

We provide a utility function, compressELT , which reduces the number of rows of an ELT by rounding and merging. This speeds up all of the calcula- tions, and is crucial for the successful completion of the Panjer approxima- tion. 

The rounding operation rounds each of the losses to a specified number d of decimal places, with d = 0 being to an integer, and d < 0 being a value with d zeros before the decimal point. Then the rounded value is multiplied by 10 d to convert it to an integer. Finally, the merge operation combines all the rows of the ELT with the same transformed loss, and adds their rates. 

Table II shows some of the original ELT, and Table III the same table after rounding to the nearest $10k (i.e. d = − 4). It is an empirical question, 

