Distribution of Selected Parameter

In this window, the probability distribution function (PDF) of the selected parameter is shown (at the cursor location in the table "Parameter Variation"). The curve is drawn according to the parameter values (average, lower and upper limit). Other distributions can also be displayed by checking the appropriate legend entry.

•Uniform (black line): for this distribution each value has equal probability. Therefore the function is a horizontal line. The value of the function is 1/(upper limit - lower limit). The expected value of the uniform distribution is (upper limit - lower limit)/2, i.e. if upper and lower limit were selected asymmetrically to the value of the deterministic simulation ("average") then the expected value of the uniform distribution is not equal to the value of the deterministic simulation.

•Normal (red curve): a normal distribution with mean value = value of deterministic simulation and a standard deviation sigma = (upper limit - lower limit)/4 is taken. The range +/- sigma can be displayed in the chart. The maximum of the probability distribution function is at the mean value.

•Lognormal (blue curve): a lognormal distribution with mean value = value of deterministic simulation and a standard deviation sigma = (upper limit - lower limit)/4 is taken. The range +/- sigma can be displayed in the chart. The maximum of the probability distribution function is at:

•Triangular distribution (green curve): its maximum of the probability distribution function is at the value of the deterministic simulation. The function is zero at lower and upper limit. The maximum value is 2/(upper limit - lower limit). The expected value of the triangular distribution is (average + upper limit + lower limit)/3. If the distribution is asymmetric then the expected value is not equal to the value of the deterministic simulation (maximum = most probable value).

Important remark: the name "average" for the value of the deterministic simulation is a bit misleading. This value is the average (or mean) for the normal and lognormal distribution. For uniform and triangular distribution this is only true if the mean value was selected symmetrically between lower and upper limit, e.g. average = (lower limit + upper limit)/2. If the limits were selected asymmetrically then the expected value resp. mean value lies at (lower limit + upper limit)/2 for the uniform distribution and at ("average" + lower limit + upper limit)/3 for the triangular distribution.