status changed; resolution set

John Maddock — Sun, 06 Apr 2014 11:02:45 GMT

status new → closed
resolution → fixed

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 ;-)

Mon, 07 Apr 2014 03:24:49 GMT

Replying to 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 ;-)

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,
HS

Boost C++ Libraries: Ticket #9834: Negative Binomial Distribution: degenerate cases

status changed; resolution set