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## ---- eval=TRUE---------------------------------------------------------------
library(bridgedist)
## ---- eval=FALSE--------------------------------------------------------------
# xaxis <- seq(-3,3,.01)
# plot(xaxis, dbridge(xaxis, phi=1/sqrt(1+3/pi^2)), type="l",
# xlab="x", ylab="density(x)")
# lines(xaxis, dnorm(xaxis))
# lines(xaxis, dlogis(xaxis, phi=sqrt(3/pi^2)))
## ---- fig.width=6, fig.cap = "Fig. 1. Probability density functions of the Gaussian, logistic and bridge, for logistic, distributions each with zero mean and unit variance."----
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")
## ---- fig.width=6, fig.cap = "Fig. 2. 10000 random variates in each panel. From left to right: the bridge distribution, the logistic with scale=1, the sum of the previous two, and the logistic with scale=1/phi. Note how similar the third and fourth panel, the application supporting the theory.", warning=FALSE, message=FALSE----
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()
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