[Numpy-discussion] Normalized histogram for data ranges 0 .. 1 returns PDF > 1
josef.pktd@gmai...
josef.pktd@gmai...
Tue Feb 2 07:44:15 CST 2010
On Tue, Feb 2, 2010 at 8:05 AM, Manos Tsagias <tsagias@gmail.com> wrote:
> Hi all,
> I'm using numpy.histogram with normed=True with 1D data ranging 0 .. 1. The
> results return probabilities greater than 1. The trapezoidal integral
> returns 1, but I'm afraid this is due to the bin assigned values. Example
> follows:
>>>> from numpy import *
>>>> a = arange(0, 1, 0.1)
>>>> histogram(a, normed=True)
> (array([ 1.11111111, 1.11111111, 1.11111111, 1.11111111, 1.11111111,
> 1.11111111, 1.11111111, 1.11111111, 1.11111111, 1.11111111]),
> array([ 0. , 0.09, 0.18, 0.27, 0.36, 0.45, 0.54, 0.63, 0.72,
> 0.81, 0.9 ]))
> Is that normal? If not, does anyone encountered that before? Ideas welcome!
> Thanks,
> Manos._
histogram with normed=True has the interpretation of a pdf of a
continuous random variable not discrete. The pdf of a continuous
distribution can be anything greater or equal zero. On [0,1] it has to
have a part that is larger than 1 unless the distribution is uniform
in order to integrate to 1.
It's a sometimes-asked-question, there are more explanations on the
mailing list.
Josef
>
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