The `bridgedist` Basics

In bridgedist: An Implementation of the Bridge Distribution with Logit-Link as in Wang and Louis (2003)

library(bridgedist)

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)
xaxis = seq(-4,4,.01)
df = data.frame( xaxis,
                 Bridge = dbridge(xaxis, phi=1/sqrt(1+3/pi^2)),
                 Normal = dnorm(xaxis),
                 Logistic = dlogis(xaxis, scale=sqrt(3/pi^2)))
melt.df <- melt(df, id.vars = "xaxis")
colnames(melt.df) <- c("x", "Distribution", "value")
ggplot(melt.df, aes(x, value, color=Distribution)) + 
  geom_line(size=1.05) + 
  ylab("Probability density function") 

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).

phi <- 0.5
df = data.frame(
                 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()

bridgedist documentation built on Dec. 28, 2022, 2:52 a.m.