The Monthly Distribution selection provides 9 distributions shown in the table below. A user specified option is also available. This method currently only works in conjunction with another outside software (i.e. HEC-WAT with the Hydrologic Sampler plugin).
Once the distribution has been selected, parameters must be specified for each month (January to December). When used within HEC-WAT with the Hydrologic Sampler Plugin, the date selection from the Hydrologic Sampler is passed to HEC-HMS which then uses the distribution parameters for the selected month to create the distribution. The selection of a model parameter value follows the sample process described in the Simple Distribution. 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}