rvtable is an R package for storing distributions of random variables in long format data frames with the rvtable class. The package provides a simplified and consistent interface for managing and manipulating random variables. The key purpose of rvtable is to carry distributions through an analysis from beginning to end where the distributions are empirically derived from a large data set that is impractical or impossible to keep in original form.

The rvtable package provides a special type of data frame subclass with associated functionality for relatively convenient storage and manipulation of random variables. The emphasis is on distributions of continuous random variables derived from relatively large samples, though discrete random variables are also handled.

# Motivation

While this package can be used for organizing small samples, there is not much point. The main motivation for rvtable is relatively seamless storage and manipulation of empirically estimated continuous probability distributions deriving from relatively large samples or data sets.

By relatively large, I mean cases where it is both substantially more statistically and computationally efficient to store and subsequently work with estimated probability distributions that are derived from and sufficiently representative of the source data than to work directly on the source data itself.

A large data set can be sampled to make it more manageable. This package provides an alternative by estimating the empirical probability density function of a continuous random variable so that the model of the distribution can be carried through analyses pipelines in place of raw observations. This allows sampling from a distribution of a random variable when and however necessary. This is particularly helpful well-estimated distributions remain much more compact and efficient than holding onto much larger amounts of data throughout a processing chain where it is ultimately not needed.

### Use case and limitations

For example, it is sometimes useful to calculate statistics as the final step in a sequence of intensive data processing operations. It could be that a product to come out of the analysis is a web application where the analyst leaves it to the user to decide interactively which variable(s) to select and what statistics to compute, what to graph and how, whether to exclude or merge data, etc. A R Shiny app is the perfect example of this.

This can lead to the problem of having far too much data to put in the application yet not being able to summarize or aggregate the data in advance sufficiently without taking too much control away from the user. When there is a lot of data involved, using a relatively efficient representation of a distribution of the data rather than raw observations or a static, relatively small sample, can help transport the relevant information from one stage of an analysis to another, particularly in a context of limited computing resources or a simple need for speed, such as in an interactive environment involving other users. At the same time, using estimated probability distributions leaves in place the ability to draw an arbitrarily large sample later when the time is right and context demands it.

The main goals of rvtable are to provide functions for storage, manipulation, and graphing of random variables in the preceding context. This is achieved through:

• Consistent use of data frame structures.
• A number of helper functions for moving between joint, marginal, and conditional distributions.
• Generic functions for providing various stock visual comparisons, such as between related marginal and conditional distributions, for various objects inheriting or deriving from rvtables.

rvtable is focused on handling distributions of continuous random variables derived from large samples, not small data sets or discrete random variables with few known or observed values, but it can still provide a consistent data structure for the context in which it is used.

It is of no benefit to known distributions with closed mathematical form expressions because there is never a need to lug a ton of such data around in the first place. For example, a random normal distribution can be sampled with rnorm at any time. rvtable is helpful for empirical samples which are large and messy, of a complicated form or mixed distributions, which cannot be reduced to a known or simple combination of known distributions, where an efficient snapshot of the distribution is helpful to avoid juggling excessive amounts of data from one analysis stage to the next while retaining sufficient distributional information.

### Details

What does an rvtable hold?

• An rvtable may contain one discrete or continuous random variable.
• The distribution of the random variable is described in a table using a values column and a probabilities column.
• Any other columns in an rvtable are ID columns and therefore should only store categorical variables.
• An rvtable is essentially a way of storing the distribution of one random variable in a data frame or, if ID columns are present in addition to the the values and probabilities columns, sections of rows of the table can be seen as a sequence of conditional distributions based on combinations of the ID variables’ levels.

Functions included in the package provide the following abilities:

• Subset specific conditional distributions from a table or marginalize over/integrate out ID variables to obtain a specified marginal distribution of the random variable
• Draw random samples from distributions.
• Invert conditional distributions, i.e., obtain the pmf of a ID variable conditional on a values of the random variable the rvtable is based on.

## Installation and bug reporting

Install the latest development version (0.6.1) from github:

install.packages("devtools")
devtools::install_github("leonawicz/rvtable")

Please file a minimal reproducible example of any clear bug at github.

## Learning rvtable

Familiarity with dplyr is recommended. An introduction vignette for rvtable is available online or:

browseVignettes(package = "rvtable")