At 03:57 PM 1/31/2007, you wrote:
Yes, this is the reason - maybe one could just make the more accurate version the default?
The default should be the one that won't get you into trouble -- i.e. the accurate version. Especially when the cost is one extra addition two extra multiplies and a divide per iteration -- rarely a significant cost compared to the process generating the samples (e.g., an input operation or a non-uniform RNG). User's who know enough and care enough to choose the dirty version intelligently could do so. Eventually you could specialize to default to the naive method if the accumulators are using exact arithmetic and you can be sure you won't overflow (remember, the naive method requires roughly twice the number of bits to store the final cumulants). Topher