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Posted to dev@commons.apache.org by Phil Steitz <ph...@steitz.com> on 2004/06/07 02:59:50 UTC
Re: [math] Getting 1.0 out the door -- tasks remaining
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.
Phil
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Re: [math] Getting 1.0 out the door -- tasks remaining
Posted by Phil Steitz <ph...@steitz.com>.
Phil Steitz 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.
I have committed changes and tests to ensure that the values in the table
above are returned, modulo correcting the following mistakes:
Both of the discrete distributions (Binomial and Hypergeometric) should
return -1 for the inverseCumulativeProbability(0). The definition that we
are using is that inverseCumulativeProbability(p) = the largest x such that
P(X <= x) <= p.
Since 0 has positive probability for both the Binomial and Hypergeometric
distributions, and the function is integer-valued, the correct value to
return in these cases is actually -1, not 0.
>
> Phil
>
>
>
>
>
>
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Re: [math] Getting 1.0 out the door -- tasks remaining
Posted by Al Chou <ho...@yahoo.com>.
--- Phil Steitz <ph...@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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