随机抽样以得出准确的总和 [英] Random sampling to give an exact sum

问题描述

我想对1000至100000之间的140个数字进行采样，以使这140个数字的总和约为200万(2000000):

I want to sample 140 numbers between 1000 to 100000 such that the sum of these 140 numbers is around 2 million (2000000):

sample(1000:100000,140)

这样:

sum(sample(1000:100000,140)) = 2000000

任何指针如何实现这一目标?

Any pointers how I can achieve this?

推荐答案

存在一种用于生成此类随机数的算法.

There exist an algorithm for generating such random numbers.

最初为 MATLAB

Originally created for MATLAB, there is an R implementation of it:

Surrogate::RandVec

MATLAB脚本注释中的引用:

Citation from MATLAB script comment:

%   This generates an n by m array x, each of whose m columns
% contains n random values lying in the interval [a,b], but
% subject to the condition that their sum be equal to s.  The
% scalar value s must accordingly satisfy n*a <= s <= n*b.  The
% distribution of values is uniform in the sense that it has the
% conditional probability distribution of a uniform distribution
% over the whole n-cube, given that the sum of the x's is s.
%
%   The scalar v, if requested, returns with the total
% n-1 dimensional volume (content) of the subset satisfying
% this condition.  Consequently if v, considered as a function
% of s and divided by sqrt(n), is integrated with respect to s
% from s = a to s = b, the result would necessarily be the
% n-dimensional volume of the whole cube, namely (b-a)^n.
%
%   This algorithm does no "rejecting" on the sets of x's it
% obtains.  It is designed to generate only those that satisfy all
% the above conditions and to do so with a uniform distribution.
% It accomplishes this by decomposing the space of all possible x
% sets (columns) into n-1 dimensional simplexes.  (Line segments,
% triangles, and tetrahedra, are one-, two-, and three-dimensional
% examples of simplexes, respectively.)  It makes use of three
% different sets of 'rand' variables, one to locate values
% uniformly within each type of simplex, another to randomly
% select representatives of each different type of simplex in
% proportion to their volume, and a third to perform random
% permutations to provide an even distribution of simplex choices
% among like types.  For example, with n equal to 3 and s set at,
% say, 40% of the way from a towards b, there will be 2 different
% types of simplex, in this case triangles, each with its own
% area, and 6 different versions of each from permutations, for
% a total of 12 triangles, and these all fit together to form a
% particular planar non-regular hexagon in 3 dimensions, with v
% returned set equal to the hexagon's area.
%
% Roger Stafford - Jan. 19, 2006

示例:

test <- Surrogate::RandVec(a=1000, b=100000, s=2000000, n=140, m=1, Seed=sample(1:1000, size = 1))
sum(test$RandVecOutput)
# 2000000
hist(test$RandVecOutput)

这篇关于随机抽样以得出准确的总和的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！