Phil Steitz wrote: > > 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 >
Hi, I also wasn't sure about the interpretation of "continuous" in ContinuousDistribution for a while. But I was incertain whether the claim was that the cumulative distribution function should be continuous or the Distribution itself should be absolutely continuous, i.e. should have a probability density function. Since density(double) had been put to ContinuousDistribution I was sure that the scope was absolutely continuous distributions. However, when allowing a generalized functions like the delta distribution (unfortunately, the term "distribution" is overloaded in mathematics) as density, then any distribution would be a ContinuousDistribution (implying that there is no need for Distribution, and DiscreteDistribution would be a special case of ContinuousDistribution). Additionally, it is not possible to implement such a generalized function meaningfully in the current setting. Thus I vote for defining ContinuousDistribution to be the interface for absolutely continuous distribution. I'm fine with a "gap" between DiscreteDistribution and ContinuousDistribution, i.e. with successors of Distribution which neither implement DiscreteDistribution nor ContinuousDistribution. Best Regards, Christian -- View this message in context: http://apache-commons.680414.n4.nabble.com/math-Continuous-Distribution-tp3950057p3950916.html Sent from the Commons - Dev mailing list archive at Nabble.com. --------------------------------------------------------------------- To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org For additional commands, e-mail: dev-h...@commons.apache.org
