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From Al Chou <hotfusion...@yahoo.com>
Subject Re: [math] Getting 1.0 out the door -- tasks remaining
Date Mon, 07 Jun 2004 13:54:14 GMT
```--- Phil Steitz <phil@steitz.com> wrote:
> J.Pietschmann wrote:
> > Phil Steitz wrote:
> >
> >> 1) Decide what to do about inverse cumulative probabilities where p =
> >> 1 (easy solution is to document and throw)
> >
> >
> > Nearly +1
> >
>
> My own "nearly +1" on this just turned to -1.  After looking some more at
> the code and thinking some more, I think that both p=1 and p=0 should be
> handled correctly in all cases.  The difficult cases are when the
> probability density function has unbounded support.  Here is what I
> propose for the values of inverseCumulativeProbability() at p=0 and p=1
> for current distributions.  Unless otherwise noted, these values are
> intented to be independent of distribution parameters.
>
> Distribution         p=0                     p=1
> ------------------------------------------------------------------
> Binomial               0               Integer.MAX_VALUE
> Chisquare              0               Double.POSITIVE_INFINITY
> Exponential            0               Double.POSITIVE_INFINITY
> F                      0               Double.POSITIVE_INFINITY
> Gamma                  0               Double.POSITIVE_INFINITY
> HyperGeometric         0               finite, parameter-dependent
> Normal       Double.NEGATIVE_INFINITY  Double.POSITIVE_INFINITY
> T            Double.NEGATIVE_INFINITY  Double.POSITIVE_INFINITY
>
> Other than the value for Chisquare with p=1 (which causes R to hang),
> these values are consistent with what R returns using the q* functions.
> It might be more convenient to return Double.MAX_VALUE, -Double.MAX_VALUE
> in place of the INFINITY's (since then we could just use
> getDomainLowerBound at 0 and 1) but this would not be correct
> mathematically.  If there are no objections, I will find a way to get the
> values above returned.

+1 to the values in the table above.  As a user I would prefer to be returned
an infinity rather than MAX_VALUE where possible (it's too bad the integer
types don't provide infinity values), because even though I would often
recognize 1e+308 or thereabouts as Double.POSITIVE_INFINITY, I would still have
to do that conversion mentally, and I would always wonder whether the returned
value was actually MAX_VALUE or just the implementation-dependent
representation of POSITIVE_INFINITY.  Also consider what would happen if the
data type were changed to float.  Then if MAX_VALUE were used, the numeric
value returned for p = 1 would differ depending on the data type.  With the
infinity values, although there's a class difference between
Double.POSITIVE_INFINITY and Float.POSITIVE_INFINITY, the concept is clearly
identical.  It's strange that BigDecimal doesn't provide infinity values,
though.  Maybe that's something Commons should address at some point.

Al

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