On 10/28/11 9:31 PM, Sébastien Brisard wrote: > Hi, > The following question might sound stupid, but occured to me while > thinking about MATH-692. So here goes. What was initially meant by > "Continuous Distribution" (as in AbstractContinuousDistribution) ? > My view on this is that the underlying random variable is defined by a > *density*, which takes *continuous* arguments. But nothing prevents > this density to be infinite at some *discrete* points (Dirac > generalized function). Then the cumulative sum would be only piecewise > C1. > When these distributions were first implemented, was it intended to > include this case?
We did not talk about these cases initially, but the intent was to include all continuous distributions. More specifically, we did not mean to leave a gap - i.e., every distribution should be either discrete or continuous, which means singular distributions need to be allowed as continuous. Phil > I should add that this case is not purely academic: it is frequently > met in the analysis of random heterogeneous materials (for example: > assemblies of hard, monodisperse spheres of radius 0.5: some > observables have such a singularity at r = 1). > > Best regards, > Sébastien > > --------------------------------------------------------------------- > To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org > For additional commands, e-mail: dev-h...@commons.apache.org > > --------------------------------------------------------------------- To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org For additional commands, e-mail: dev-h...@commons.apache.org
