[FIXED] Gamma CDF and inverse CDF not producing compliment values

Issue

Why isn't the inverse gamma function producing the original x value?

Code

x = 0.2
alpha = 2
u = sp.stats.gamma.cdf(x, alpha)
x1 = sp.stats.invgamma.cdf(x, alpha)
print "x: ", x
print "G: ", u
print "GInv:", x1

Output

x:  0.2
G:  0.0175230963064
GInv: 0.0404276819945

When I perform a similar operation in Excel I get the same value back.

=GAMMADIST(Q15,2,1,TRUE)
=GAMMA.INV(Q16,2,1)

Output

0.2
0.017523096
0.2

I know I'm just overlooking something, but I can't seem to figure out why the inverse isn't working for me.

Solution

In scipy.stats, gamma is the gamma distribution and invgamma is the inverse gamma distribution. These are two different probability distributions--see the wikipedia article for the relation of the inverse gamma to the gamma distribution.

If you want the inverse of gamma.cdf, use gamma.ppf. (The acronym ppf stands for percent point function, which is another name for the quantile function.)

For example,

In [7]: p = gamma.cdf([1, 2, 3], 0.5)

In [8]: gamma.ppf(p, 0.5)
Out[8]: array([ 1.,  2.,  3.])

Answered By - Warren Weckesser