'pi6.txt' is the one-million digit text file vexp is the expected-value vector vobservedfreq_7 is the observed frequency vector for the digit '7' vobservedprop_7 is the observed proportion vector for the digit '7' dlknorm.m is the Matlab code file for the eponymous function dpnorm.m ibid DLKnorm_screenshot shows the results for sample digits 0 and 7. DPnorm_screenshot ibid The code files dpnorm and dlknorm can either be read as text files using a text editor, or used to generate results in a Matlab environment. If the latter, put both the files and the pi-file into the same directory and invoke as usual. The screenshots give samples for '0' and '7'. Other digits give quantitatively similar results.