This is a readme file for the python codes developed
In support of the linear fits to Poisson data with the
Cash statistic
References: Bonamente and Spence (2022) 
'A semi--analytical solution to the maximum--likelihood fit of 
Poisson data to a linear model using the Cash statistic'
Journal of Applied Statistics, 49, 3, 522-552
https://doi.org/10.1080/02664763.2020.1820960

Covariance matrix was developed in Bonamente (2023) submitted
'Linear regression for Poisson count data: 
A new semi--analytical method with applications to COVID-19 events'

The main function is 

   bestFitLinear(data,hasGap,dataGap)

where data has the format specified in the test case below.
If the data have "gaps", they can be specified with the additional
parameter. See test case #2 for an example, which is the general
case of data with non-uniform binning and gaps.

The main function implementing an analytical form for the
covariance matrix in the linear fit is in

   covMatrixCT(lambdaHat, aHat,data)

where CT stands for Cameron and Trivedi, authors of the book
"Regression Analysis of Count Data" 2nd Ed. Cambridge (2013)


Test cases: 
python3 cstatLinear.py xbinCovidDeaths.dat dataCovidperDayDeaths.txt paramsCovidDeaths.txt
python3 cstatLinear.py xbinCovidDeaths1-2.dat dataCovidperDayDeaths1-2.txt paramsCovidDeaths1-2.txt



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Note: these codes were updated from those used in the
original 2022 paper.