In vincenzocoia/distionary: Create and Evaluate Univariate Probability Distributions

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(distionary)

One purpose of distplyr is to handle the menial distribution-related calculations for you. Just specify a distribution once, and there is no need to manage its components anymore.

Example: want to compute the variance of a Uniform(-1, 1) distribution, get the 0.25- and 0.75-quantiles, and generate a sample of size 10?

Without distplyr:

a <- -1
b <- 1
# Look up formula for variance:
(b - a) ^ 2 / 12
# Get quantiles:
qunif(c(0.25, 0.75), min = a, max = b)
# Get sample of size 10:
runif(10, min = a, max = b)

With distplyr:

d <- dst_unif(-1, 1)
variance(d)
eval_quantile(d, at = c(0.25, 0.75))
realise(d, 10)

Functional Representations of a Distribution

A distribution can be represented by different functions, such as a density function, a cumulative distribution function, and others. In distplyr, you can:

• evaluate the function directly by calling eval_*;
• evaluate the function and enframe results together with the function arguments with enframe_*; or
• get the function itself using get_*.

Here are the representations and the corresponding distplyr functions:

| Quantity | distplyr Functions | |----------------------------------|-----------------------------------| | Cumulative Distribution Function | eval_cdf(), get_cdf(), enframe_cdf() | | Survival Function | eval_survival(), get_survival(), enframe_survival() | | Quantile Function | eval_quantile(), get_quantile(), enframe_quantile() | | Hazard Function | eval_hazard(), get_hazard(), enframe_hazard() | | Cumulative Hazard Function | eval_chf(), get_chf(), enframe_chf() | | Probability density function | eval_density(), get_density(), enframe_density() | | Probability mass function | eval_pmf(), get_pmf(), enframe_pmf() |

These functions all take a distribution object as their first argument, and eval_* and enframe_* have a second argument named at indicating where to evaluate the function. The at argument is vectorized.

Here is an example of evaluating the hazard function and the random sample generator of a Uniform(-1,1) distribution, and enframing the density:

eval_hazard(d, at = 0:10)
enframe_density(d, at = 0:10)
set.seed(10)

enframe() works particularly well with tibbles and tidyr::unnest():

# half_marathon <- tribble(
#   ~ person, ~ race_time_min,
#   "Vincenzo", dst_norm(130, 25),
#   "Colleen", dst_norm(110, 13),
#   "Regina", dst_norm(115, 20)
# ) 
# half_marathon %>% 
#   mutate(quartiles = map(race_time_min, enframe_quantile, at = 1:3 / 4)) %>% 
#   unnest(quartiles)

Drawing a random sample

To draw a random sample from a distribution, use the realise() or realize() function:

realise(d, n = 5)

You can read this call as "realise distribution d five times". By default, n is set to 1, so that realizing a distribution converts it to a numeric draw:

realise(d)

This default is especially useful when working with distributions in a tibble:

# half_marathon %>% 
#   mutate(actual_time_min = map_dbl(race_time_min, realise))

Perhaps surprisingly, distplyr does not consider realise() as a functional representation of a distribution, even though random sampling falls into the same family as the stats::p*/d*/q*/r* functions. This is because it's impossible to perfectly describe a distribution based on a sample.

Properties of Distributions

Distributions have various numeric properties. Common examples are the mean and variance, but there are many others as well.

Below is a table of the properties incorporated in distplyr:

| Property | distplyr Function | |----------|---------------------| | Mean | mean() | | Median | median() | | Variance | variance() | | Standard Deviation | sd() | | Skewness | skewness() | | Excess Kurtosis | kurtosis_exc() | | Kurtosis | kurtosis_raw() | | Extreme Value (Tail) Index | evi() |

Here are some properties of our original Uniform(-1, 1) distribution:

mean(d)
stdev(d)
evi(d)

vincenzocoia/distionary documentation built on March 5, 2024, 3:13 a.m.