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Hi all,
I am a newbie to Python and would like to genereate some numbers
according to geometric distribution. However, the Python Random package
seems do not have implemented functionality. I am wondering is there
exist any other libraries that can do this job?
Thanks a lot,
Da  
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On 20060723 17:12:20, My***********@gmail.com wrote:
I am a newbie to Python and would like to genereate some numbers
according to geometric distribution. However, the Python Random package
seems do not have implemented functionality. I am wondering is there
exist any other libraries that can do this job?
The usual way is to generate standard random numbers (linear distribution)
and then apply whatever transformation you need to generate the desired
distribution.
Gerhard  
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Gerhard Fiedler wrote:
On 20060723 17:12:20, My***********@gmail.com wrote:
>I am a newbie to Python and would like to genereate some numbers according to geometric distribution. However, the Python Random package seems do not have implemented functionality. I am wondering is there exist any other libraries that can do this job?
The usual way is to generate standard random numbers (linear distribution)
and then apply whatever transformation you need to generate the desired
distribution.
That only works if there is such a transformation.
The geometric distribution and many others have been implemented in numpy: http://www.scipy.org/NumPy
In [1]: from numpy import random
In [2]: random.geometric(0.5, size=100)
Out[2]:
array([1, 5, 2, 3, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 2, 3, 3, 1, 1, 1, 1, 1,
2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1,
4, 1, 1, 1, 2, 1, 2, 3, 2, 1, 1, 1, 1, 1, 3, 1, 1, 2, 6, 1, 1, 3, 2,
1, 1, 2, 1, 1, 7, 2, 1, 1, 2, 1, 1, 2, 4, 1, 2, 1, 4, 2, 1, 1, 2, 1,
4, 2, 1, 1, 3, 1, 3, 1])

Robert Kern
"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
 Umberto Eco  
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Robert Kern wrote:
Gerhard Fiedler wrote:
On 20060723 17:12:20, My***********@gmail.com wrote:
I am a newbie to Python and would like to genereate some numbers
according to geometric distribution. However, the Python Random package
seems do not have implemented functionality. I am wondering is there
exist any other libraries that can do this job?
The usual way is to generate standard random numbers (linear distribution)
and then apply whatever transformation you need to generate the desired
distribution.
That only works if there is such a transformation.
The geometric distribution and many others have been implemented in numpy:
http://www.scipy.org/NumPy
In [1]: from numpy import random
In [2]: random.geometric(0.5, size=100)
Out[2]:
array([1, 5, 2, 3, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 2, 3, 3, 1, 1, 1, 1, 1,
2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1,
4, 1, 1, 1, 2, 1, 2, 3, 2, 1, 1, 1, 1, 1, 3, 1, 1, 2, 6, 1, 1, 3, 2,
1, 1, 2, 1, 1, 7, 2, 1, 1, 2, 1, 1, 2, 4, 1, 2, 1, 4, 2, 1, 1, 2, 1,
4, 2, 1, 1, 3, 1, 3, 1])

Robert Kern
"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
 Umberto Eco
Thanks a lot. I will try it out.
But I am still surprised because the default Random package in Python
can generate so few discrete random distritbuions, while it can
generate quite a few continuous distribution, including some not very
common one.
Da  
P: n/a
 My***********@gmail.com writes:
But I am still surprised because the default Random package in Python
can generate so few discrete random distritbuions, while it can
generate quite a few continuous distribution, including some not very
common one.
It looks pretty simple to transform the uniform distribution to the
geometric distribution. The formula for its cdf is pretty simple:
cdf(p,n) = (1p)**(n1)*p
For fixed p, if the cdf is c, we get (unless I made an error),
n = log(c, 1p)  1
So choose a uniform point c in the unit interval, run it through that
formula, and round up to the nearest integer.
See http://en.wikipedia.org/wiki/Geometric_distribution
for more about the distribution.  
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Paul Rubin <http://ph****@NOSPAM.invalidwrites:
n = log(c, 1p)  1
I meant n = log(c/p, 1p)  1
sorry.  
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Paul Rubin wrote:
Paul Rubin <http://ph****@NOSPAM.invalidwrites:
> n = log(c, 1p)  1
I meant n = log(c/p, 1p)  1
sorry.
import random
from math import ceil, log
def geometric(p):
""" Geometric distribution per Devroye, Luc. _NonUniform Random Variate
Generation_, 1986, p 500. http://cg.scs.carleton.ca/~luc/rnbookindex.html
"""
# p should be in (0.0, 1.0].
if p <= 0.0 or p 1.0:
raise ValueError("p must be in the interval (0.0, 1.0]")
elif p == 1.0:
# If p is exactly 1.0, then the only possible generated value is 1.
# Recognizing this case early means that we can avoid a log(0.0) later.
# The exact floating point comparison should be fine. log(eps) works just
# dandy.
return 1
# random() returns a number in [0, 1). The log() function does not
# like 0.
U = 1.0  random.random()
# Find the corresponding geometric variate by inverting the uniform variate.
G = int(ceil(log(U) / log(1.0  p)))
return G

Robert Kern
"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
 Umberto Eco  
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Robert Kern <ro*********@gmail.comwrites:
G = int(ceil(log(U) / log(1.0  p)))
I usually owuld write that as int(ceil(log(U, 1.0  p))).  
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Paul Rubin wrote:
Robert Kern <ro*********@gmail.comwrites:
> G = int(ceil(log(U) / log(1.0  p)))
I usually owuld write that as int(ceil(log(U, 1.0  p))).
Knock yourself out. I was cribbing from my C implementation in numpy.

Robert Kern
"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
 Umberto Eco  
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Robert Kern <ro*********@gmail.comwrites:
I usually owuld write that as int(ceil(log(U, 1.0  p))).
Knock yourself out. I was cribbing from my C implementation in numpy.
Oh cool, I thought you were pasting from a Python implementation. No prob.   This discussion thread is closed Replies have been disabled for this discussion.   Question stats  viewed: 9329
 replies: 9
 date asked: Jul 23 '06
