Two-Piece Distributions (R package)

Overview

twopiece is an R package for the family of two-piece distributions, a flexible class of unimodal distributions constructed by joining two rescaled half-densities of a symmetric baseline distribution at the mode. This simple construction introduces asymmetry while preserving the tail behaviour and shape of the chosen baseline, making two-piece distributions a tractable and interpretable alternative to standard symmetric models.

Given a unimodal symmetric (about 0) probability density function $f$ from the location-scale family, the two-piece density is:

$$s(x;, \mu, \sigma_1, \sigma_2, \delta) = \frac{2}{\sigma_1 + \sigma_2} \begin{cases} f\left(\dfrac{x - \mu}{\sigma_1};, \delta\right), & x < \mu, \\ f\left(\dfrac{x - \mu}{\sigma_2};, \delta\right), & x \geq \mu, \end{cases}$$

where $\mu$ is the mode, $\sigma_1, \sigma_2 &gt; 0$ are scale parameters governing the left and right tails respectively, and $\delta$ is an optional shape parameter of the baseline $f$. Setting $\sigma_1 = \sigma_2$ recovers the symmetric baseline. Common choices of baseline include the normal, Student-t, Laplace, and logistic distributions, among others.

Installation

# install.packages("devtools")
devtools::install_github("FJRubio67/twopiece")
library(twopiece)

Main functions

The package provides density (d), distribution (p), quantile (q), and random sampling (r) functions for two-piece distributions with three or four parameters:

Function	Description
dtp3 / ptp3 / qtp3 / rtp3	Two-piece distributions with 3 parameters ($\mu$, $\sigma_1$, $\sigma_2$)
dtp4 / ptp4 / qtp4 / rtp4	Two-piece distributions with 4 parameters ($\mu$, $\sigma_1$, $\sigma_2$, $\delta$)

The baseline distribution is passed as a function argument (e.g. FUN = dnorm, FUN = dt), making the package compatible with any symmetric unimodal baseline available in R.

Three parameterisations of asymmetry are supported via the param argument:

param	Parameterisation
"tp"	Two-piece: separate scale parameters $(\sigma_1, \sigma_2)$
"eps"	Epsilon-skew: single scale $\sigma$ and skewness parameter $\gamma \in (-1, 1)$
"isf"	Inverse scale factors: single scale $\sigma$ and skewness parameter $\gamma \in (0, \infty)$

For full documentation: ?dtp3, ?dtp4

Quick example

library(twopiece)

# Two-piece normal: asymmetric with heavier right tail
x <- seq(-5, 10, length.out = 500)
plot(x, dtp3(x, mu = 0, par1 = 1, par2 = 3, FUN = dnorm, param = "tp"),
     type = "l", ylab = "Density", main = "Two-piece Normal")

# Random sampling
sim <- rtp3(1000, mu = 0, par1 = 1, par2 = 3, FUN = rnorm, param = "tp")

Tutorials

• The family of two-piece distributions — mathematical background and examples
• twopiece R package — package walkthrough

Related packages

• DTP — Double two-piece distributions (R)
• TPSAS — Two-piece sinh-arcsinh distributions (R)
• FlexBinReg — Binary regression with two-piece link functions

License

This package is licensed under the MIT License.