The Normal distribution has the property of being symmetric around its 50%-fractile. The distribution is particularly well suited to model uncertainty of quantities being a sum of many “underlying” variables. The range of the distribution is the set of all real numbers. However, a Normally distributed variable will with very high probability get a value not more than 3 standard deviations away from the 50%-fractile. Thus, in cases where the standard deviation is very small compared to the mean, the Normal distribution may be a good approximation even if the actual range of the variable is only a limited interval.
In the Normal distribution the key numbers, “a”, “b” and “c” are interpreted as follows:
“a” = The 10%-fractile.
“b” = The 50%-fractile.
“c” = The 90%-fractile.
To get a sensible distribution, the specified values must satisfy:
“a” < “b” < “c”
DynRisk will adjust the numbers further to make the fractiles fit the fractiles of a Normal distribution.
The Normal distribution will fit the specified fractiles perfectly, i.e., no further adjustments are needed if the fractiles satisfy the following equation:
“b” - “a” = “c” - “b”
Note that in this case, the “b” value is the arithmetic mean of the “c” and the “a” value.
Assume e.g., that the following key numbers are specified:
“a” = 0.5
“b” = 1.0
“c” = 1.5
In this case we get that:
“b” - “a” = “c” - “b” = 0.5
Thus, the Normal distribution fits the specified fractiles perfectly.
