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")

Four Type of Patterns



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