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Here are some common ratios.
We want to draw numbers such that we have some mean \(b\), and that the possible maximum and minimum value drawn are at most \(a\) times apart. Given \(b\) and \(a\), solve for \(x\).
\[ f(x) = \frac{b+x}{b-x} - a = 0 \]
\[ b \cdot a - x \cdot a = b + x \\ b \cdot a - b = x + x \cdot a \\ b \left(a - 1\right) = x \left( a+ 1\right) \\ x = \frac{b\left(a-1\right)}{a+1}\\ \]
Uniformly draw
b <- 100
a <- 2
x <- (b*(a-1))/(a+1)
ar_unif_draws <- runif(100, min=b-x, max=b+x)
fl_max_min_ratio <- max(ar_unif_draws)/min(ar_unif_draws)
cat('fl_max_min_ratio =', fl_max_min_ratio, 'is close to a =', a, '\n')## fl_max_min_ratio = 1.965658 is close to a = 2