Chapter 3 RANDOM VARIATE GENERATION - USNA

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3-1 Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of RANDOM variables having known distributions. These values are often called RANDOM variates. As was the case in the drive-in window example above, the starting place for RANDOM VARIATE GENERATION is usually the GENERATION of RANDOM numbers, which are RANDOM variates that are uniformly distributed on the interval from 0 to 1 (uniform [0, 1]). Inverse Transform Method The table look-up technique that we used earlier may be used whenever the simulation is being done by hand or by using a spreadsheet. It is also used in some simulation languages due to the speed with which it can be implemented on a digital computer. One of its disadvantages is that it takes a great deal of effort to implement on a computer, and thus is seldom used whenever the simulation is written in a high level language such as C or FORTRAN. The procedure basically uses the inverse of the cumulative distribution function F given in a table rather than a formula.

3-1 Chapter 3 RANDOM VARIATE GENERATION ... 3-8 RANDOM VARIATE GENERATION Figure 3.6: Generating Gamma Random Variates ... make use of Excel’s NORMDIST function, as shown in Figure 3.8, to find the cumulative probability of the random variable being less than the bin value. These values are in Column G in

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