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:
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