如何在R中加上条件约束来生成随机数？ [英] how to generate random numbers with conditons impose in R?

问题描述

我想生成500个满足以下条件的a，b和c组合

I would like to generate 500 different combination of a,b,and c meeting the following conditions

1. a + b + c = 1并且


2. a< b< c

这是生成随机数的基本示例，但是，我需要根据上述条件生成它。

here is a basic sample of generating random numbers, however, I need to generate it based on aforementioned conditions.

Coeff = data.frame(a=runif(500, min = 0, max = 1),
b=runif(500, min = 0, max = 1),
c=runif(500, min = 0, max = 1))

推荐答案

myrandom <- function(n) {
  m <- matrix(runif(3*n), ncol=3)
  m <- cbind(m, rowSums(m)) # rowSums is efficient
  t(apply(m, 1, function(a) sort(a[1:3] / a[4])))
}

演示：

set.seed(2)
(m <- myrandom(5))
#           [,1]      [,2]      [,3]
# [1,] 0.1099815 0.3287708 0.5612477
# [2,] 0.1206611 0.2231769 0.6561620
# [3,] 0.2645362 0.3509054 0.3845583
# [4,] 0.2057215 0.2213517 0.5729268
# [5,] 0.2134069 0.2896015 0.4969916
all(abs(rowSums(m) - 1) < 1e-8) # CONSTRAINT 1: a+b+c = 1
# [1] TRUE
all(apply(m, 1, diff) > 0)      # CONSTRAINT 2: a < b < c
# [1] TRUE

注意：

• 我对 sum to 1的检验不只是 == 1 ，因为IEEE-754和 R FAQ 7.31 ，建议任何浮点测试都应是不等式，而应等同于相等性；如果您测试 == 1 ，您最终会发现似乎无法满足的情况：

• my test for "sum to 1" is more than just ==1 because of IEEE-754 and R FAQ 7.31, suggesting that any floating-point test should be an inequality vice a test for equality; if you test for ==1, you will eventually find occurrences where it does not appear to be satisfied:

set.seed(2)
m <- myrandom(1e5)
head(which(rowSums(m) != 1))
# [1]  73 109 199 266 367 488
m[73,]
# [1] 0.05290744 0.24824770 0.69884486
sum(m[73,])
# [1] 1
sum(m[73,]) == 1
# [1] FALSE
abs(sum(m[73,]) - 1) < 1e-15
# [1] TRUE
max(abs(rowSums(m) - 1))
# [1] 1.110223e-16

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