CONTRIBUTION OF PRESENT RESEARCH TO UNCERTAINTY ASSESSMENT METHODS - Modelling Uncertainty in Flood Forecasting Systems - page 76

Figure 4.16. Transformation between CDF and MF.
As shown in Figure 4.16, P 0 is the value of P X at x = x 0 . This results in " ( x = x 0 )=1, which
is normally interpreted as the most credible value for the MF. Therefore, x 0 should preferably
be one of the central values of the PDF, i.e. mean, median or mode. If the x 0 is taken as
the median of the distribution, P 0 becomes 0.5 and the transformations will take the form
(4.65)
(4.66)
Therefore, with these transformations Equations (4.43) and (4.45) are equivalent to
Equations (4.54) and (4.55) respectively, when
(4.67)
The equivalency between Equations (4.44) and (4.57) (subtraction operation) and
between Equations (4.46) and (4.58) (division operation) can be established, if Equations
(4.57) and (4.58) are modified as follows:
(4.68)
(4.69)