# how to quantify the patterns of multivariate distribution (e.g. clustered in the center vs. spread out all over the place)?

by Ray Yang   Last Updated October 01, 2018 01:19 AM

I am wondering if there exists a well-established way to quantify such patterns (please see the graph)? I guess there should be multiple ways to quantify it or multiple aspects that can be quantified.

The R code for generating the plot

``````  set.seed(100)
par(mfrow = c(2, 2))

a1 <- rnorm(n = 100, mean = 0, sd = 1)
b1 <- rnorm(n = 100, mean = 0, sd = 1)
plot(a1 , b1, main = "denser in the center")

a2 <- runif(n = 100, min = -2, max = 2)
b2 <- runif(n = 100, min = -2, max = 2)
plot(a2 , b2, main = "'balanced' all over the place")

a3 <- c(rnorm(n = 50, mean = -1, sd = 0.5), rnorm(n = 50, mean = 1, sd = 0.5))
b3 <- c(rnorm(n = 50, mean = -1, sd = 0.5), rnorm(n = 50, mean = 1, sd = 0.5))
plot(a3 , b3, main = "denser in two corners")

b4 <- c(rnorm(n = 50, mean = -1, sd = 0.3), runif(n = 50, min = -2, max = 2))
plot(a3 , b4, main = "denser in one coner, spread out elsewhere")
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