the CSTAT or Cash values given for these parameters are largely different than the ones obtained by fitting the data.
sim = normal_sample( num=1000 )
plot_cdf( sim[ :, 0] )
plotting the cummulative distribution of the statistic values provides immediate visualization of
the best fit statistics in comparison to the simulations. The best fit statistic values should be close to the 0.5 in the cdf, so about 50% of the values. If the best fit statistics value is not close to 50% in the cdf plot then the fit is not good.
Using numpy we can also check the minimum and median of the simulated distribution in comparison to the best fit values.
# first check the current statistics, then check the simulations:
numpy.min( sim[ :, 0 ])numpy.median( sim[ :, 0 ])