The Triangular distribution is called so because of its triangular shaped density function. The range of the distribution is a bounded interval of real numbers.
In the triangular distribution the key numbers, 窶彗窶, 窶彙窶 and 窶彡窶 are interpreted as follows:
窶彗窶 = The 0%-fractile.
窶彙窶 = The mode of the density function (the value corresponding to the maximum of the density).
窶彡窶 = The 100%-fractile.
To get a sensible distribution, the specified values must satisfy:
窶彗窶 < 窶彙窶 < 窶彡窶
DynRisk will reorder the numbers if they do not satisfy these requirements. No further adjustments are needed.
The probability, p, of having a value less than or equal to the 窶彙窶 value is given by:
p = (窶彙窶 - 窶彗窶) / (窶彡窶 - 窶彗窶).
Note that if 窶彙窶 is the arithmetical mean of 窶彡窶 and 窶彗窶, it is also equal to the 50%-fractile of the distribution.
Assume e.g., that the following key numbers are specified:
窶彗窶 = 0.5
窶彙窶 = 1.0
窶彡窶 = 3.0
In this case we get that:
p = (1.0 - 0.5) / (3.0 - 0.5) = 0.2
Thus, in this case 窶彙窶 value is equal to the 20%-fractile of the distribution.
