[SciPy-user] Is this a bug in stats.geom.pmf?

[Stefan van der Walt]

On Mon, Jun 25, 2007 at 02:59:09PM -0600, Fernando Perez wrote:
> Hi all,
> 
> just curious.  The stats.geom docstring says:
> 
>     Geometric distribution
> 
>     geom.pmf(k,p) = (1-p)**(k-1)*p
>     for k >= 1
> 
> But I see this:
> 
> In [10]: k,p = 2.0,0.5
> 
> In [11]: (1-p)**(k-1)*p
> Out[11]: 0.25
> 
> In [12]: stats.geom.pmf(k,p)
> Out[12]: array(0.125)
> 
> However:
> 
> In [13]: stats.geom.pmf(k-1,p)
> Out[13]: array(0.25)
> 
> 
> Is this an off-by-one bug, or am I misreading something here?

I read now in wikipedia that:

"""
In probability theory and statistics, the geometric distribution is
either of two discrete probability distributions:

    * the probability distribution of the number X of Bernoulli trials
      needed to get one success, supported on the set { 1, 2, 3, ...},
      or

    * the probability distribution of the number Y = X − 1 of failures
      before the first success, supported on the set { 0, 1, 2, 3,
      ... }.

Which of these one calls "the" geometric distribution is a matter of
convention and convenience.
"""

So, do we simply pick one and stick with it?

Cheers
Stéfan