The Normal distribution

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.