# [Numpy-discussion] non-uniform discrete sampling with given probabilities (w/ and w/o replacement)

Christopher Jordan-Squire cjordan1@uw....
Wed Aug 31 13:51:13 CDT 2011

```In numpy, is there a way of generating a random integer in a specified
range where the integers in that range have given probabilities? So,
for example, generating a random integer between 1 and 3 with
probabilities [0.1, 0.2, 0.7] for the three integers?

I'd like to know how to do this without replacement, as well. If the
probabilities are uniform, there are a number of ways, including just
shuffling the data and taking the first however-many elements of the
shuffle. But this doesn't apply with non-uniform probabilities.
Similarly, one could try arbitrary-sampling-method X (such as
inverse-cdf sampling) and then rejecting repeats. But that is clearly
sub-optimal if the number of samples desired is near the same order of
magnitude as the total population, or if the probabilities are very
skewed. (E.g. a weighted sample of size 2 without replacement from
[0,1,2] with probabilities [0.999,.00005, 0.00005] will take a long
time if you just sample repeatedly until you have two distinct
samples.)

I know parts of what I want can be done in scipy.statistics using a
discrete_rv or with the python standard library's random package. I
would much prefer to do it only using numpy because the eventual
application shouldn't have a scipy dependency and should use the same
random seed as numpy.random.

(For more background, what I want is to create a function like sample
in R, where I can give it an array-like of doo-hickeys and another
array-like of probabilities associated with each doo-hickey, and then
generate a random sample of doo-hickeys with those probabilities. One
step for that is generating ints, to use as indices, with the same
probabilities. I'd like a version of this to be in numpy/scipy, but it
doesn't really belong in scipy since it doesn't

-Chris JS
```