Click for printer friendely version of this HowTo Generating Random Variables From a Discrete Distribution For this, let us consider the following hypothetical discrete distribution: $$f(x) = \left\{ \begin{array}{ll} 0 & x < 0 0.25 & 0 < x < 1 0.5 & 1 < x < 2 0.25 & 2 < x < 3 0 & 3 < x \end{array} \right.$$ (3.8.1) Thus, with this distribution, you would expect a quarter of the data points in a random sample to come from between 0 and 1, half to come from between 1 and 2 and the remaining quarter to come from between 2 and 3. In order to simulate a random sample from this distribution, we can map it to an interval ranging between 0 and 1. This can be done by simply taking length of each interval, multiplying it by its probability and storing the new value in an array. For this distribution, the first index of the array would contain 0.25, the second 0.5 and the third 0.25. To generate the random sample, select a random number between 0 and 1 and check if it is greater than the value in the first index. If it is not, then the point falls between 0 and 1 in our distribution. We can then choose another random number between 0 and 2 to determine which particular value it is. If the first random number is greater than the value at the first index, then we check to see it if it is greater than the values at the first and second indices combined (0.25 + 0.5) and continue this procedure until we have established which segment in the distribution it comes from and then determine the exact value from that segment by choosing another random number. This particular example has been coded in octave and the program can be found in Appendix A.3. A histogram of the output can be seen in Figure 3.8.4 where the sample size was set to 200. Figure: A histogram of 200 simulated random variables from generate_discretes.m. Click for printer friendely version of this HowTo

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