Calculating Permutation Entropy without Permutations

Table 5

Arithmetic entropy, permutation entropy, and normalized entropies for the first 1 000 000 digits of .

D	2	3	4	5
AE	1.369	3.477	6.067	8.992
PE	0.993	2.563	4.536	6.816
NAE	0.864	0.940	0.974	0.990
NPE	0.993	0.992	0.989	0.987

Entropy is given in bits. NAE is calculated as AE/, where is taken from the bottom row of Table 4.