NAME

       Algorithm::Numerical::Sample - Draw samples from a set

SYNOPSIS

           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;

DESCRIPTION

       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.

   A: "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.

   B: "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.

CORRECTNESS PROOFS

   Algorithm A.
       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).

   Algorithm B.
       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).

LITERATURE

       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.

REFERENCES

       [1] C. T. Fan, M. E. Muller and I. Rezucha, J. Amer. Stat. Assoc.  57 (1962), pp 387 - 402.

       [2] T. G. Jones, CACM 5 (1962), pp 343.

       [3] D.  E.  Knuth:  The  Art  of Computer Programming, Volume 2, Third edition.  Reading: Addison-Wesley,
           1997. ISBN: 0-201-89684-2.

DEVELOPMENT

       The      current      sources      of      this       module       are       found       on       github,
       <git://github.com/Abigail/algorithm--numerical--sample.git>.

AUTHOR

       This package was written by Abigail, cpan@abigail.be.

COPYRIGHT and LICENSE

       Copyright (C) 1998, 1999, 2009, Abigail.

       Permission  is  hereby  granted,  free  of  charge,  to  any person obtaining a copy of this software and
       associated documentation files (the "Software"), to deal in the Software without  restriction,  including
       without  limitation  the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
       copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to  the
       following conditions:

       The  above  copyright  notice  and  this permission notice shall be included in all copies or substantial
       portions of the Software.

       THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR  IMPLIED,  INCLUDING  BUT  NOT
       LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO
       EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
       IN  AN  ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR
       THE USE OR OTHER DEALINGS IN THE SOFTWARE.

perl v5.10.1                                       2010-01-12                  Algorithm::Numerical::Sample(3pm)