[SciPy-dev] fix for ncx2 bug?

Neal Becker ndbecker2@gmail....
Wed Jun 17 12:53:07 CDT 2009

josef.pktd@gmail.com wrote:

> On Wed, Jun 17, 2009 at 1:08 PM, Neal Becker<ndbecker2@gmail.com> wrote:
>> josef.pktd@gmail.com wrote:
>>> On Wed, Jun 17, 2009 at 10:45 AM, Neal Becker<ndbecker2@gmail.com>
>>> wrote:
>>>> As reported earlier, there is a bug in ncx2 that causes a strange
>>>> discontinuity.
>>>> Is there a patch available?
>>> It's a ticket, but it could take some time until someone finds all the
>>> imprecision for "outlier" cases in scipy.special.
>>> I'm not sure these functions are even designed to have a high
>>> precision, because for distributions such as chisquare or ncx2, that
>>> are primarily used for test statistics, it make only sense to report a
>>> few digits.
>>> I would have recommended ncx2.veccdf for your case, but a quick check
>>> showed that over a large range ncx2.veccdf and ncx2.cdf only agree up
>>> to 1e-8. For ncx2.cdf close to one, there might also be a precision
>>> loss.
>>> What's your use case that you need ncx2 at high precision?
>>> Josef
>> I'm using this to compute what's often called "Receiver Operating
>> Characteristic", which is a signal detection problem.  You may see over
>> some range that probability of miss or false detection is quite low. 
>> Probably you don't really care about accuracy here, but it's making the
>> plots look bad.
> If speed doesn't matter too much, you can still use veccdf, I don't
> think it's more accurate but it is smooth, no discontinuities and it
> also goes to 1 in the upper tail.
> veccdf is a private method, that avoids the argument check, but as
> long as you call it with valid arguments you get good solutions, and
> it is vectorized (based on np.vectorize). The generic methods are
> pretty heavily tested, so besides slower speed from the numerical
> integration, I wouldn't expect any problems.
> In contrast to central chisquare, I didn't see any formulas that would
> allow a direct calculation of the ncx2.cdf as function of some other
> special functions.
> Josef

I'm no expert on this.  I do see 2 refs:

Continuous Univariate Distributions, Vol 2, 2nd edition, Johnson, Kotz,  
Balakrishnan has an entire chapter on the subject.


The code says:
            // Computes the complement of the Non-Central Chi-Square
            // Distribution CDF by summing a weighted sum of complements
            // of the central-distributions.  The weighting factor is
            // a Poisson Distribution.
            // This is an application of the technique described in:
            // Computing discrete mixtures of continuous
            // distributions: noncentral chisquare, noncentral t
            // and the distribution of the square of the sample
            // multiple correlation coeficient.
            // D. Benton, K. Krishnamoorthy.
            // Computational Statistics & Data Analysis 43 (2003) 249 - 267

I see that the 1st ref above also talks about the fact that cdf on ncx2 can 
be obtained as weighted sum of central distributions, but it also goes on to 
give other methods of calculation.

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