
98 Simulation Technologies in Networking and Communications
4.3.1 r/s sTaTisTiC: DefiniTion anD algoriThms
The rescaled adjusted range, range over standard deviation, or simply R/S statistic is one of the old-
est methods for estimating the Hurst-index, H, in long-memory and self-similar time series [23–27].
It was initially developed by E. Hurst while studying nonstandard behavior in the Nile River. The
range in (τ
i
,τ
i
+ n) is dened for a process Y(t) according to the following relation:
Rn Wn Wn
i
un
i
un
i
(,):
,
††
τττ=
()
()
−
⎡
⎢
⎤
⎥
≤≤ ≤≤00
(4.18)
where
WnYuYuEn
ii ii
(,)( )()(,).
ττ
=+−−
E(τ
i
,n) denotes the sample mean with index τ
i
in the inter ...