The Uniform distribution is called so because its density function is constant over its range. The range of the distribution is a bounded interval of real numbers. The probability of getting a value within a specific subinterval of the range, is equal to the length of the subinterval divided by the length of the range. Thus, clearly a uniform distribution is uniquely determined by its range, i.e., its 0%-fractile and its 100%-fractile.
In the Uniform 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 50%-fractile
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. After the reordering, only 窶彗窶 and 窶彡窶 are used to fit the Uniform distribution. Specifically the range of the distribution is chosen to be the interval from 窶彗窶 to 窶彡窶. The 窶彙窶 value is adjusted so that it becomes equal to the 50%-fractile of the fitted distribution, i.e., the arithmetical mean of 窶彡窶 and 窶彗窶.
Assume e.g., that the following key numbers are specified:
窶彗窶 = -0.5
窶彙窶 = 1.0
窶彡窶 = 3.5
Since these numbers are ordered as they should, there is no need for any reordering. The Uniform distribution ranging from (-0.5) to 3.5 is chosen. Finally the 窶彙窶 value is adjusted from 1.0 to:
