Algorithm::Numerical::Sample - Draw samples from a set
use Algorithm::Numerical::Sample qw /sample/; @sample = sample (-set => [1 .. 10000], -sample_size => 100); $sampler = Algorithm::Numerical::Sample::Stream -> new; while (<>) {$sampler -> data ($_)} $random_line = $sampler -> extract;
This package gives two methods to draw fair, random samples from a set. There is a procedural interface for the case the entire set is known, and an object oriented interface when the a set with unknown size has to be processed.
sample (set => ARRAYREF [,sample_size => EXPR])
The sample
function takes a set and a sample size as arguments. If the sample size is omitted, a sample of 1
is taken. The keywords set
and sample_size
may be preceeded with an optional -
. The function returns the sample list, or a reference to the sample list, depending on the context.
Algorithm::Numerical::Sample::Stream
The class Algorithm::Numerical::Sample::Stream
has the following methods:
new
This function returns an object of the Algorithm::Numerical::Sample::Stream
class. It will take an optional argument of the form sample_size => EXPR
, where EXPR
evaluates to the sample size to be taken. If this argument is missing, a sample of size 1
will be taken. The keyword sample_size
may be preceeded by an optional dash.
data (LIST)
The method data
takes a list of parameters which are elements of the set we are sampling. Any number of arguments can be given.
extract
This method will extract the sample from the object, and reset it to a fresh state, such that a sample of the same size but from a different set, can be taken. extract
will return a list in list context, or the first element of the sample in scalar context.
Crucial to see that the sample
algorithm is correct is the fact that when we sample n
elements from a set of size N
that the t + 1
st element is choosen with probability (n - m)/(N - t)
, when already m
elements have been choosen. We can immediately see that we will never pick too many elements (as the probability is 0 as soon as n == m
), nor too few, as the probability will be 1 if we have k
elements to choose from the remaining k
elements, for some k
. For the proof that the sampling is unbiased, we refer to [3]. (Section 3.4.2, Exercise 3).
It is easy to see that the second algorithm returns the correct number of elements. For a sample of size n
, the first n
elements go into the reservoir, and after that, the reservoir never grows or shrinks in size; elements only get replaced. A detailed proof of the fairness of the algorithm appears in [3]. (Section 3.4.2, Exercise 7).
Both algorithms are discussed by Knuth [3] (Section 3.4.2). The first algoritm, Selection sampling technique, was discovered by Fan, Muller and Rezucha [1], and independently by Jones [2]. The second algorithm, Reservoir sampling, is due to Waterman.
C. T. Fan, M. E. Muller and I. Rezucha, J. Amer. Stat. Assoc. 57 (1962), pp 387 - 402.
T. G. Jones, CACM 5 (1962), pp 343.
D. E. Knuth: The Art of Computer Programming, Volume 2, Third edition. Reading: Addison-Wesley, 1997. ISBN: 0-201-89684-2.
The current sources of this module are found on github, git://github.com/Abigail/algorithm--numerical--sample.git.
This package was written by Abigail, cpan@abigail.be.
Copyright (C) 1998, 1999, 2009, Abigail.
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