On 10/29/11 7:16 AM, cwinter wrote: > 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.
Thinking about this some more, I agree. Phil > 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 > > --------------------------------------------------------------------- To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org For additional commands, e-mail: dev-h...@commons.apache.org
