Tweedie distributions

We often encounter distributions that are not normal, I often encounter poisson and gamma distributions as well as distributions with an inflated zero value all of which belong to the family of tweedie distributions. When changing the parameter \(p\) which can take values between 0 and 2 ( p == 0 gaussian, p == 1 poisson, p == 2 gamma) we can sample the different tweedie distributions.

suppressWarnings({
  suppressPackageStartupMessages({
    require(tidyverse)
    require(tweedie)
    require(ggridges)
  })
})
df = tibble( p = seq(1,2,0.1) ) %>%
  mutate( data = map(p, function(p) rtweedie(n = 500
                                             , mu = 1
                                             , phi = 1
                                             , power = p )  ) ) %>%
  unnest(data)

df %>%
  ggplot( aes(x = data) )+
    geom_histogram(bins = 100, fill = '#77773c') +
    facet_wrap(~p, scales = 'free_y')

Joyplot

We will now transform these distributions into a joyplot in the style of the Joy Divisions album Unknown Pleasurs cover art.

We will use ggridges formerly known as ggjoy.

joyplot = function(df){

  p = df %>%
    ggplot(aes(x = data, y = as.factor(p), fill = ..x.. ) ) +
      geom_density_ridges_gradient( color = 'white'
                                   , size = 0.5
                                   , scale = 3) +
      theme( panel.background = element_rect(fill = 'white')
             , panel.grid = element_blank()
             , aspect.ratio = 1
             , axis.title = element_blank()
             , axis.text = element_blank()
             , axis.ticks = element_blank()
             , legend.position = 'none') +
     xlim(-1,5) +
     scale_fill_viridis_c(option = "inferno") 
  
  return(p)

}

joyplot(df)
## Picking joint bandwidth of 0.24

I order to distribute them a bit better over the x-axis we will transform them using a sine wave pattern.

df = tibble( p = seq(1,2,0.05)
             , rwn = row_number(p)
             , sin = sin(rwn) ) %>%
  mutate( data = map(p, function(p) rtweedie(500
                                             , mu = 1
                                             , phi = 1
                                             , power = p)  ) ) %>%
  unnest(data) %>%
  filter( data <= 4) %>%
  mutate( data = ( 4 * abs( sin(rwn) ) ) - data )


joyplot(df)
## Picking joint bandwidth of 0.206