Civil Engineering Reference
In-Depth Information
Interpreting this as a probability density function‚ the mean and variance are
given by
Since the gamma distribution has a mean of
and a variance of
these
values can be fitted as follows
The approximate step response is then given by
and its median can be determined from a preconstructed two-dimensional lookup
table that depends on and When the input is a saturated ramp‚ sim-
ilar techniques as for PRIMO may be used to find the delay from a three-
dimensional lookup table‚ parameterized by
and the input transition time.
The WED metric.
The above methods inspired [LKA02] to use a Weibull
distribution instead of the gamma distribution‚ yielding the advantage of re-
quiring smaller lookup tables. The algorithm for the WEibull-based Delay
(WED) metric is simple and is listed in Table 3.1 (a); for details of the deriva-
tions‚ the reader is referred to [LKA02]. The computation uses the
function‚
which is has the property‚ for
therefore‚ by storing the
value of
in a table‚ this property can be used to find
for any arbitrary
