Standard distance

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Student resources for Statistical methods for geographers

Standard distance simulations

library(haffutils)
library(ggplot2)
library(ggforce)

## assign values to x
set.seed(11)
x <- rnorm(10000)

## assign values to y
set.seed(12)
y <- rnorm(10000)

df <- data.frame(x=x, y=y)

# visualize
pretty_dens(x)
pretty_dens(y)

## percentage of x coordinates between -1 and 1
length(x[x<1 & x>-1])/length(x)

## percentage of x coordinates between -2 and 2
length(x[x<2 & x>-2])/length(x)

## percentage of x coordinates between -3 and 3
length(x[x<3 & x>-3])/length(x)

## percentage of y coordinates between -1 and 1
length(y[y<1 & y>-1])/length(y)

## percentage of y coordinates between -2 and 2
length(y[y<2 & y>-2])/length(y)

## percentage of y coordinates between -3 and 3
length(y[y<3 & y>-3])/length(y)

## create function for standard distance
st_dist <- function(x, y) {
  sqrt(sum(((x - mean(x))^2)/length(x)) + (sum((y - mean(y))^2)/length(y)))
}

## plot points
pts_plotted <- ggplot(df, aes(x=x, y=y)) +
  geom_point(size = 0.3) +
  coord_fixed()

pts_plotted

## draw standard distances as circles
pts_plotted +
  ## one standard distance
  geom_circle(aes(x0 = mean(x),
                  y0 = mean(y),
                  r = st_dist(x,y))) +
  ## two standard distances
  geom_circle(aes(x0 = mean(x),
                  y0 = mean(y),
                  r = 2*st_dist(x,y))) +
  ## three standard distances
  geom_circle(aes(x0 = mean(x),
                  y0 = mean(y),
                  r = 3*st_dist(x,y)))

## calculate distance from mean center to each point
df$dist <- sqrt((mean(x) - x)^2 + (mean(y) - y)^2)

## percentage of points falling within one standard distance of the mean center
nrow(df[df$dist < 1 * st_dist(x, y),])/nrow(df)

## percentage of points falling within two standard distances of the mean center
nrow(df[df$dist< 2 * st_dist(x, y),])/nrow(df)

## percentage of points falling within three standard distances of the mean center
nrow(df[df$dist < 3 * st_dist(x,y),])/nrow(df)

Standard distance in 3d