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 窶忖nderlying窶 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, 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:
窶彗窶 < 窶彙窶 < 窶彡窶
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:
窶彙窶 - 窶彗窶 = 窶彡窶 - 窶彙窶
Note that in this case, the 窶彙窶 value is the arithmetic 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 = 1.5
In this case we get that:
窶彙窶 - 窶彗窶 = 窶彡窶 - 窶彙窶 = 0.5
Thus, the Normal distribution fits the specified fractiles perfectly.
