Crystal Ball function
The Crystal Ball function, named after the Crystal Ball Collaboration, is a probability density function commonly used to model various lossy processes in high-energy physics such as Bremsstrahlung by electrons. It consists of a Gaussian core portion and a power-law low-end tail, below a certain threshold. The function itself and its first derivative are both continuous.
The Crystal Ball function is given by:
where
with the error function erf.
The parameters of the function are:
- is a normalization factor
- defines the point where the PDF changes from a power-law to a Gaussian distribution
- is the power of the power-law tail
- and are the mean and the standard deviation of the Gaussian