Asymmetric Power Distribution (APD) family of densities extends the Generalized Power Distribution to cases where the data exhibits asymmetry.
It contains the asymmetric Gaussian and Laplace densities as special cases.
In the paper entitled "Asymmetric Power Distribution: Theory and Applications to Risk Measurement", I provide a detailed description of the properties of an APD random variable, such as its quantiles and expected shortfalls.
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Asymmetric Power Distribution
Here is some Matlab code that I have written for my paper "Asymmetric Power Distribution: Theory and Applications to Risk Measurement":
APDpdf.m : APD probability density function
APDcdf.m : APD cumulative density function
APDinv.m : APD quantiles
APDrnd.m : APD random number generator
APDstat.m : statistical moments of an APD random variable
APDes.m : expected shortfall of an APD random variable
... and several sample programs:
plotAPDpdf.m : 2D-plots of APD density
plotAPDpdfsurf.m : 3D-plots of APD density
plotAPDstat.m : 2D-plots of APD moments
plotAPDstatsurf.m : 3D-plots of APD moments
testAPDpdf.m : some numerical examples
plotAPDes.m : 2D-plots of APD expected shortfall
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