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January 13, 2018 00:09
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Discussing how often a string with two cuts will form a triangle
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n_sims <- 1e5 | |
breaking_convention <- "all_at_once" # or stick_breaking | |
if (breaking_convention == "stick_breaking"){ | |
break_locations <- matrix(runif(n = n_sims), ncol=1) | |
sorted_break_locations <- cbind(break_locations, matrix(runif(n = n_sims, min = break_locations, max=1), ncol=1)) | |
} else { | |
break_locations <- matrix(runif(n = 2*n_sims), ncol=2) | |
sorted_break_locations <- t(apply(break_locations, 1, sort)) | |
} | |
segment_lengths <- cbind(sorted_break_locations[,1], | |
sorted_break_locations[,2] - sorted_break_locations[,1], | |
1 - sorted_break_locations[,2]) | |
sorted_segment_lengths <- t(apply(segment_lengths, 1, sort)) | |
head(sorted_segment_lengths) | |
is_triangle <- function(x){ | |
as.logical(x[3] < (x[2] + x[1])) | |
} | |
triangles <- apply(sorted_segment_lengths, 1, is_triangle) | |
binom.test(x = rev(table(triangles))) |
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