The Simple Distribution selection provides 11 distributions shown in the table below. A user specified option is also available. The uncertainty within a parameter or rainfall depth can be defined using one of the 11 distribution provided. Once the distribution has been selected and the parameters defined, the selection of a value from the distribution begins with HEC-HMS generating a pseudo-random number from a uniform distribution between 0 and 1. This pseudo-random number represents a probability. The next step involves using this probability along with the inverse cumulative distribution function (inverse CDF) of the target distribution to obtain a value. Essentially, the inverse CDF maps the probability to a specific value within the desired distribution, allowing us to translate the uniformly generated random number into a value that follows the characteristics of the target distribution. The user determines the number of random samples performed. HEC-HMS generates the seed value associated with the time the Uncertainty Compute Type was created. However, this initial seed value can be modified if required.
f(x)=\begin{cases} 0, & x < a,\\ \frac{2(x-a)}{(b-a)(c-a)}, & a \le x < c,\\ \frac{2}{b-a}, & x = c,\\ \frac{2(b-x)}{(b-a)(b-c)}, & c < x \le b,\\ 0, & b < x. \end{cases}