library(distplyr)
#> 
#> Attaching package: 'distplyr'
#> The following object is masked from 'package:stats':
#> 
#>     sd
library(magrittr)
library(tibble)

You’re able to make a wide range of probability distributions using distplyr’s manipulation functions, but you’ll need to start with more standard, basic distributions first. There are typically three use cases for building a basic distribution:

  1. Parametric families
  2. Empirical distributions
  3. Manually specified distributions

1. Parametric Families

These include distributions like Normal, Exponential, Poisson, etc.

distplyr includes distributions present in base R’s r*/p*/d*/q* selection of distributions. For example, a Normal distribution in base R has associated functions rnorm() etc. In distplyr:

dst_norm(0, 1)
#> Gaussian Distribution
#> 
#> Parameters:
#> # A tibble: 3 x 2
#>   parameter value
#>   <chr>     <dbl>
#> 1 mean          0
#> 2 variance      1
#> 3 sd            1
#> 
#> Number of Discontinuities:  0

distplyr also includes other common distributions not present in base R, such as a generalized Pareto distribution:

dst_gpd(0, 1, 1)
#> Generalized Pareto Distribution
#> 
#> Parameters:
#> # A tibble: 3 x 2
#>   parameter value
#>   <chr>     <dbl>
#> 1 location      0
#> 2 scale         1
#> 3 shape         1
#> 
#> Number of Discontinuities:  0

November 2020: Until this package gains some stability in its structure, there will be a limited number of these distributions – but there will be plenty available in the not-too-distant future.

2. Empirical Distributions

Whereas base R only has the ecdf() function to handle empirical distributions, distplyr provides full functionality with stepdst() (soon to be called something like dst_emp()). Empirical distribution of hp values in the mtcars dataset:

(hp <- stepdst(hp, data = mtcars))
#> Step Distribution
#> 
#> Number of Discontinuities:  22

The “step” in the name comes from the cdf:

plot(hp, "cdf", n = 501)

You can also weigh the outcomes differently. This is useful for explicitly specifying a probability mass function, as well as for other applications such as using kernel smoothing to find a conditional distribution. Here is an estimate of the conditional distribution of hp given disp = 150, with cdf depicted as the dashed line compared o the marginal with the solid line:

K <- function(x) dnorm(x, sd = 25)
hp2 <- stepdst(hp, data = mtcars, weights = K(disp - 150))
plot(hp, "cdf", n = 1001)
plot(hp2, "cdf", n = 1001, lty = 2, add = TRUE)

The weighting provides us with a far more informative prediction of hp when disp = 150 compared to the loess, which just gives us the mean:

mean(hp2)
#> [1] 109.961

With a distribution, you can get much more, such as this 90% prediction interval:

eval_quantile(hp2, at = c(0.05, 0.95))
#> [1]  62 175

Here’s the proportion of variance that’s reduced compared to the marginal:

1 - variance(hp2) / variance(hp)
#> [1] 0.8031741

3. Manually specified distributions

It’s common to specify a distribution by explicitly specifying a representation, like a density, cdf, etc.

To do this, start with an empty distribution by calling distribution(), and then set_ the representation of interest. Here’s the random variable with cdf given by the sqrt() function:

(manual <- distribution() %>% 
  set_cdf(sqrt))
#>  Distribution
#> 
#> Parameters:
#> # A tibble: 0 x 0
#> 
#> Number of Discontinuities:
plot(manual, "cdf", from = 0, to = 1)

Down the road, you’ll also be able to use purrr-style functions:

distribution() %>% 
    set_cdf(~ sqrt(.x))