## The argument `scale` has been replaced with `phi` in this version.
## The top of page 77o in Wang Louis 2003 states phi is not a scale.
## Please start using the `phi` argument now.
Recreate the plot from Wang and Louis (2003) where the Bridge, Normal, and Logistic all have unit variance and mean 0 with ggplot2:
library(reshape2) library(ggplot2) = seq(-4,4,.01) xaxis = data.frame( xaxis, df Bridge = dbridge(xaxis, phi=1/sqrt(1+3/pi^2)), Normal = dnorm(xaxis), Logistic = dlogis(xaxis, scale=sqrt(3/pi^2))) <- melt(df, id.vars = "xaxis") melt.df colnames(melt.df) <- c("x", "Distribution", "value") ggplot(melt.df, aes(x, value, color=Distribution)) + geom_line(size=1.05) + ylab("Probability density function")
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0. ## ℹ Please use `linewidth` instead.
The implication is that a random variable from a Bridge distribution plus random variable from a standard logistic distribution is a logistic random variable with a scale greater than one (1/phi).
<- 0.5 phi = data.frame( df Bridge = rbridge(1e5, phi=phi), Std_Logistic = rlogis(1e5), BridgePlusStd_Logistic = rbridge(1e5, phi=phi) + rlogis(1e5), Logistic = rlogis(1e5, scale=1/phi) )<- melt(df) melt.df colnames(melt.df) <- c("Distribution", "value") ggplot(melt.df, aes(value)) + facet_grid(.~Distribution) + geom_histogram()