Re: [Boost-bugs] [Boost C++ Libraries] #9834: Negative Binomial Distribution: degenerate cases

Subject: Re: [Boost-bugs] [Boost C++ Libraries] #9834: Negative Binomial Distribution: degenerate cases
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2014-04-07 03:24:49

#9834: Negative Binomial Distribution: degenerate cases
--------------------------------------+-------------------------
  Reporter:  HS <tan@…>               |      Owner:  johnmaddock
      Type:  Feature Requests         |     Status:  closed
 Milestone:  To Be Determined         |  Component:  math
   Version:  Boost Development Trunk  |   Severity:  Problem
Resolution:  fixed                    |   Keywords:
--------------------------------------+-------------------------

Comment (by HS <tan@…>):

 Replying to [comment:1 johnmaddock]:
 > See
 https://github.com/boostorg/math/commit/0c01f682eb9c562d3cca6372c0aa8e68951decd1

 >
 > I haven't made the quantile for probability 1 zero in the corner case
 you gave: rather it's always at infinity.  I think this is more
 consistent, though there are an infinite number of "correct" answers for
 this case ;-)
 [[br]]
 Dear John,

 Thank you (and your team) for the great work!

 I will not quibble with you about this---it is an edge case which is
 generally not very interesting in the applied world.  However, as a
 teacher (was) of probability classes, the inverse CDF (or quantile) at p
 of a distribution F, to us, is the infimum of all x such that F(x) >= p;
 in this degenerate case of a discrete distribution, this is 0.  And one
 will also find this is so on R too:

 {{{
 > qnbinom(1,3,1,lower.tail=FALSE)
 [1] 0
 > qnbinom(1,3,1,lower.tail=TRUE)
 [1] 0
 > qnbinom(0,3,1,lower.tail=FALSE)
 [1] 0
 > qnbinom(0,3,1,lower.tail=TRUE)
 [1] 0
 }}}

 Mathmatica 9, on the other hand, says the following:

 {{{
 In[1]:= Quantile[NegativeBinomialDistribution[3,1],0]
 Out[1]= 0

 In[2]:= Quantile[NegativeBinomialDistribution[3,1],1]
 Out[2]= Infinity
 }}}

 But it is very easy for anyone to work around the decision here if he or
 she disagrees with it.   :)

 With best regards,[[br]]
 HS

-- 
Ticket URL: <https://svn.boost.org/trac/boost/ticket/9834#comment:2>
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