# Combined Distribution

### Introduction

When modeling an uncertain variable based on expert opinion, it can often occur that different experts independently provide a different estimate. So one ends up with a number of distinct distributions: one for each expert's opinion.

Combined Distribution combines these "individual" distributions into one final distribution that incorporates all the information.

The empirical distributions are usually used in modelling expert opinions, such as Uniform, Triangle, PERT, ModPERT, Relative, CumulA, etc.

The Combined Distribution interface allows modeling the estimates of as many experts as needed, and also allows assigning weights to each of the different opinions. The level of confidence that we assign to each of the experts is proportional to the weight that we give to that expert.

Combining expert opinions is explained in more detail here.

### Window Elements

On the upper left, you can add distributions to combine.

To add a new distribution field to the list, click anywhere in the white area.

To remove a distribution from the list, click the X button below.

The chart on top of the window shows the separate distributions that each of the experts provide their estimates on. They are scaled according to the weights assigned to the experts, so that the area under all curves sums up 1. If there are three experts and they are assigned the following weights: {1,2,4} then the area under the first expert's curve is 1/7, second expert's curve - 2/7 and the last expert's (the one with most credibility) is 4/7.

The upper graph shows the separate distributions that need to be combined.

The graph at the bottom shows the Combined distribution - the constructed distribution that takes into account the opinions of all experts.

Different types of output can be specified by selecting the appropriate option under the preview graph:

• Object - to insert the constructed distribution as a distribution Object in the spreadsheet.

• Simulation - (default) to generate random values from the distribution.

• f(x) and F(x) - to calculate the probability density function and the cumulative distribution function of some x value(s) (an extra parameter x values will appear on the left side of the window).

• F-1(U) - to calculate the inverse cumulative when a U-value is entered.

For explanations about other fields, buttons, graphs and summary statistics tables in this window, see

### Useful tips and tricks

The output of ModelRisk windows always corresponds to VoseFunctions (the functions ModelRisk adds to Excel) being entered into one or more spreadsheet cells.

You can always re-open the window for a ModelRisk function that is in a spreadsheet cell by using View Function. Select the spreadsheet cell and then select View Function from the ModelRisk menu/toolbar/ribbon.