dirichlet: The Dirichlet Distribution

In dkahle/dirichlet: The Dirichlet Distribution

The Dirichlet Distribution

Description

Density, distribution function, quantile function and random generation for the dirichlet distribution.

Usage

ddirichlet(x, alpha, log = FALSE)

rdirichlet(n, alpha)

Arguments

x	vector of quantiles.
alpha	dirichlet alpha parameter (numeric vector with positive entries)
log	logical; if TRUE, probabilities p are given as log(p).
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The functions (d/r)dirichlet simply wrap those of the standard (d/r)gamma R implementation, so look at, say, dgamma for details.

See Also

dgamma; these functions just wrap the (d/r)gamma functions.

Examples

ddirichlet(c(.5,.5), c(.5, .5))
dbeta(.5, .5, .5)

rdirichlet(3, c(1, 1))     # rows sum to 1
rdirichlet(3, c(1, 1, 1))  # rows sum to 1
rowSums(rdirichlet(3, c(1, 1, 1)))


library(dplyr)
library(ggplot2); theme_set(theme_bw())

samples <- rdirichlet(2e3, rep(1,3))
head(samples)

# project the points into two dimensions
bary_samples <- simp2bary(samples) %>% as.data.frame %>% tbl_df
names(bary_samples) <- c("dim1", "dim2")
qplot(dim1, dim2, data = bary_samples) +
  coord_equal()




# visualize a density
f <- function(v) ddirichlet(v, c(20, 10, 5))
mesh <- simplex_mesh(.0025) %>% as.data.frame %>% tbl_df
mesh$f <- mesh %>% apply(1, function(v) f(bary2simp(v)))
  
p <- ggplot(mesh, aes(x, y)) +
  geom_raster(aes(fill = f)) +
  coord_equal(xlim = c(0,1), ylim = c(0, .85))
p
  
points <- rdirichlet(1e3, c(20, 10, 5)) %>% simp2bary %>% 
  as.data.frame %>% tbl_df %>% rename(x = V1, y = V2)
p + geom_point(data = points, color = "orange", alpha = .3)
  

dkahle/dirichlet documentation built on June 4, 2023, 4:51 a.m.