Function Repository Resource:

CrystalBallDistribution

Define a continuous probability distribution characterized by a Gaussian core and a power-law tail

Contributed by: Arnoud Buzing

ResourceFunction["CrystalBallDistribution"][α,n,x_,σ]

computes the Crystal Ball distribution for the given shape parameters.

Details

The Crystal Ball distribution is named after the Crystal Ball collaboration, a particle physics experiment that used a detector called the Crystal Ball to measure particle interactions. The distribution is often used in high-energy physics for fitting data distributions that have a Gaussian shape with an additional power-law tail.

The α parameter determines the transition point between the Gaussian core and the power-law tail. It affects how quickly the distribution changes from the Gaussian behavior to the power-law behavior.

The n parameter is the tail parameter and controls the shape of the power-law tail. A larger value of n results in a steeper tail, meaning the influence of the power-law component diminishes more rapidly.

The

parameter is the mean or central value around which the Gaussian core is centered. It shifts the entire distribution along the x-axis without affecting its shape.

The σ parameter is the standard deviation of the Gaussian core, controlling the spread of the distribution. It widens or narrows the Gaussian component without affecting the tail.