logUniform.R

library(pipeR)
library(ggplot2)

dens <- function(x) {
  sapply(x, function(x)(
    if (x >= 1 && x <= exp(1)) {
        1 / x
    } else {
        0
    }
  ))
}

dens2 <- function(x) {ifelse(0 <= x & x <= 1, 1, 0)}

stepSize <- 0.00001

domainData <- data.table(x = seq.int(from=-stepSize, to = 3, by = stepSize))

domainData <-
domainData[, Y := dens(x)
          ][, X := dens2(x)
          ][, Y_CDF := cumsum(Y * stepSize)
          ][, X_CDF := cumsum(X * stepSize)] %>>%
melt.data.table(id.vars = c('x')) %>>%
`[`(variable %in% c('Y', 'X'), type := 'density') %>>%
`[`(variable %in% c('Y_CDF', 'X_CDF'), type := 'cdf')

ggplot(data = domainData, aes(x=x, color=variable, y=value)) +
geom_line() +
facet_grid(type~.) +
theme_bw()

ggsave("~/loguniform.png", units = "in", width=4, height=6)