library(dplyr)
library(ggplot2)

dist_maker <- function(d, m, s){
    d <- eval(parse(text=d[1]))
    function(x){
        d(x, m, s)
    }
}

lnorm_sd_from_mean_mode <- function(mu, mo){
    sqrt((mu^3 * (mo/mu)^(1/3))/mo - mu^2)
}

dlnorm_mean_sd <- function(x, m, s){
    l_m <- log(m / sqrt(1 + s^2/m^2))
    l_s <- sqrt(log(1 + s^2/m^2))
    dlnorm(x, l_m, l_s)
}

data.frame(distribution = c('A', 'B', 'C', 'D'),
           mu = c(50, 60, 60, 60),
           sigma = c(10, 10, 15, lnorm_sd_from_mean_mode(60, 50)),
           dfunc = c("dnorm", "dnorm", "dnorm", "dlnorm_mean_sd")
           ) %>%
               do(cbind(.[rep(seq(1, nrow(.)), each = 200),],
                        x = seq(20, 120, length.out = 200))
               ) %>% group_by(distribution) %>%
               mutate(density = dist_maker(dfunc, mu, sigma)(x)) %>%
               ggplot(aes(x = x, y = density, color = distribution)) + geom_line() +
               scale_color_brewer(type = 'qual', palette = 3) +
               facet_grid(distribution ~ .) + theme_bw()