Today I released a new version of my twopiece Python package in pip. The **two-piece distributions **result from joining (at the mode) the corresponding halves of a continuous, symmetric distribution using the same location parameter $\mu$ but possibly different:

- scale parameters $\sigma_1$ and $\sigma_2$
- shape parameters $\delta_1$ and $\delta_2$

on each side of the mode.

This idea can be seen in the following graphs where we can see in blue and pink the two half densities and the resulting two-piece density in green.

## Release Notes

twopiece 1.2.0 now supports the following three families of two-piece distributions:

- Two-Piece Scale (already included in older versions)
- Two-Piece Shape (new!)
- Double Two-Piece (new!)

In addition, new display functions were added for each family. These functions will help you to visualise quickly any of the supported distributions. Take a look at these features in the Demo included in the gist below (also in my GitHub).

## twopiece 1.2.0 Library Demo

To see this Demo directly in GitHub click here!

## Further References

- For technical details on the two-piece families of distributions we refer the reader to the following two publications which were used as reference for our implementation.
- Inference in Two-Piece Location-Scale Models with Jeffreys Priors published in Bayesian Analysis Volume 9, Number 1 (2014), 1-22.
- Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions published in Electronic Journal of Statistics, Volume 9, Number 2 (2015), 1884-1912.

- For the R implementation we refer to the following packages: twopiece, DTP, and TPSAS
- For more information on the two-piece normal distributions take a look at these two former entries:

[…] the parameters for each projection in its Monetary Policy Report. Using these parameters and the twopiece Python package, we can plot the projected density functions to visualise the entire distribution […]