[Numpy-discussion] QQ Plot in Python and Noncentral Chisquare

Thu Aug 16 09:55:08 EDT 2012

On Thu, Aug 16, 2012 at 9:05 AM, Yi, Chuang <chuang.yi at bankofamerica.com> wrote:
> Thank you Josef, df can be less than 1 as long as it is nonnegative:
>
> http://stat.ethz.ch/R-manual/R-patched/library/stats/html/Chisquare.html
>
> Here is an example in R:
>
>> Z0<-rchisq(2,df=0.5,ncp =2)
>> Z0
> [1] 0.5056454 2.0427540
>
> Thanks, Chuang
>
> -----Original Message-----
> From: numpy-discussion-bounces at scipy.org [mailto:numpy-discussion-bounces at scipy.org] On Behalf Of josef.pktd at gmail.com
> Sent: Wednesday, August 15, 2012 9:59 PM
> To: Discussion of Numerical Python
> Subject: Re: [Numpy-discussion] QQ Plot in Python and Noncentral Chisquare
>
> On Wed, Aug 15, 2012 at 10:59 AM, Yi, Chuang
> <chuang.yi at bankofamerica.com> wrote:
>> Hello,
>>
>>
>>
>> I am a new user of Python. I have a couple of questions that would
>> appreciate your guidance!
>>
>>
>>
>> QQ Plot in Python: I could not find any functions in either Numpy or Scipy
>> to do QQ Plot of two vectors of data. For example, in Matlab, one could just
>> call qqplot(X,Y), which will generate the QQ plot of vector X against vector
>> Y. Would you please let me know which python package has similar
>> functionality?
>> Noncentral Chisquare: it looks to me that in Numpy and Scipy, the noncentral
>> chisquare distribution only allows Integer degree of freedom. For example,
>> the following code will produce an error message. In R, however, it also
>> allows non-integer degree of freedom. Would you please let me know which
>> python package has similar functionality?
>>
>> data = numpy.random.noncentral_chisquare(0.5, 2, 100)
>> ValueError: df <= 0
>
> restriction is >1 not integer
>
>>>> np.random.noncentral_chisquare(1, 2, 100)
> Traceback (most recent call last):
>   File "<stdin>", line 1, in <module>
>   File "mtrand.pyx", line 1957, in
> mtrand.RandomState.noncentral_chisquare
> (numpy\random\mtrand\mtrand.c:9847)
> ValueError: df <= 0
>
>>>> np.random.noncentral_chisquare(1.0001, 2, 100)
> array([  5.75083221,   1.08050491,   0.69267684,   1.37806056,
>          2.39899   ,   0.31415666,   2.9202386
>
>
> I don't know if the >1 restriction is justified or could be dropped.

A quick look at numpy\random\mtrand\distributions.c :

double rk_noncentral_chisquare(rk_state *state, double df, double nonc)
{
    double Chi2, N;

    Chi2 = rk_chisquare(state, df-1);
    N = rk_gauss(state) + sqrt(nonc);
    return Chi2 + N*N;
}

It uses df-1 for chisquare, which means df>1 for non-central is required here.

So there needs to be another way of generating non-central chisquare
for 0<df<=1.

rk_noncentral_f uses rk_noncentral_chisquare so it will have the same
limitation.

(I don't have the time to look into this.)

Josef

>
> Josef
>
>>
>>
>>
>> Thank you very much,
>>
>>
>>
>> Regards,
>>
>> Chuang
>>
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