The Lognormal distribution is a distribution concentrated on the set of positive numbers. The distribution is particularly well suited to model uncertainty of quantities being a product of many 窶忖nderlying窶 variables. The Lognormal distribution is often used to model uncertainty about variables representing cost.
In the Lognormal distribution the key numbers, 窶彗窶, 窶彙窶 and 窶彡窶 are interpreted as follows:
窶彗窶 = The 10%-fractile.
窶彙窶 = The 50%-fractile.
窶彡窶 = The 90%-fractile.
To get a sensible distribution, the specified values must satisfy:
0 < 窶彗窶 < 窶彙窶 < 窶彡窶
DynRisk will adjust the numbers further to make the fractiles fit the fractiles of a Lognormal distribution.
The Lognormal distribution will fit the specified fractiles perfectly, i.e., no further adjustments are needed if the fractiles satisfy the following equation:
窶彙窶 / 窶彗窶 = 窶彡窶 / 窶彙窶
Note that in this case, the 窶彙窶 value is the geometric mean of the 窶彡窶 and the 窶彗窶 value.
Assume e.g., that the following key numbers are specified:
窶彗窶 = 0.5
窶彙窶 = 1.0
窶彡窶 = 2.0
In this case we get that:
窶彙窶 / 窶彗窶 = 窶彡窶 / 窶彙窶 = 2.0
Thus, the Lognormal distribution fits the specified fractiles perfectly.