Part 2. MM4XL Tools > 1. Strategic Tools > Risk Analyst > 2. Simulation Never heard of it > Random numbers

## Risk Analyst

### Random numbers

Random numbers are the building blocks of scenario modeling. They are numbers extracted randomly from a given range of values in order to generate custom variables used in scenario models.

Excel generates random numbers between 0 and 1 with the function =Rand(). Readers interested in the subject of random number generation with Excel may refer to the MS Excel User Manual. Also, the paper from Keeling and Pavur Numerical accuracy issues in using Excel for simulation studies is an interesting one that compares the accuracy of random numbers generated with different software packages, including various versions of MS Excel.

Really random numbers satisfy two important properties: they are independent from each other and they are uniformly distributed.

Independent random numbers means that if a random number is generated in one Excel cell and then a second random number is generated in a second cell, there is no relationship between the two. That is, the second number tells us nothing about the first number.

How frequently a random number is extracted depends on the kind of distribution and on its parameters. For instance, the function =RAND assigns the same probability of occurrence to all values in the range, as the previously mentioned function mmRANDBETWEEN does. This is called a Uniform distribution and it is often shown as U(0,1). Then, there are functions that return values with a certain shape. The mmTRI(0%, 5%, 10%) in the picture below returns values in the range 0%-10%, and 5% is the modal value. Running this function many times would return some 50% of the random numbers in the range 0%-5% and 50% of the values would lie between >5% and 10%. Testing the property of independence of random numbers can be done using the MM4XL function mmHISTO as shown with the first chart in the section What are Probability Distribution Functions. The second property of random numbers, uniformity, can be tested by checking that 50% of random numbers are equal or smaller than 0.5 and the remaining 50% of the numbers are larger that 0.5. However, this is less simple to test because there may be (or may not be) combinations of large and small numbers that violate the assumption of independence.

The Risk Analyst tool of MM4XL software provides 25 different sheet functions that can be used to simulate random numbers from as many different probability distributions. With such equipment available, managers can model virtually any process in order to support critical business decisions.

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