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 repository hosts code to calculate C, C_m, and the theoretical mean and variance of C_m. For the sake of organization, implementations in different languages live in different branches.
| Language | Branch | Note |
|---|---|---|
| C | C |
|
| Python | python |
On PyPi (pip install cashstatistic) |