cashstatistic

Utility functions related to the Cash statistic

The Poisson distribution is

P(x|mu) = exp(-mu) mu^x / x!

The Cash statistic is defined to be the model (mu) dependent part of -2ln(P), analogous to the role that chi^2 plays for the Gaussian distribution,

C = 2( mu - x*ln(mu) ).

A modified version,

C_m = 2( mu - x + x*ln(x/mu) ),

is equivalent to C for parameter inference (i.e. has the same dependence on mu), and also has the nice property of becoming equivalent to chi^2 when x is large. Kaastra (2017) was kind enough to provide approximate expressions for the mean and variance of C_m, which can be used to determine whether the actual C_m corresponding to a fitted model is indicative of a good fit (just as chi^2 does for the Gaussian distribution).

This package contains python code to calculate C, C_m, and the theoretical mean and variance of C_m. The GitHub repo contains implementations in other languages.