1. Empirical Distributions

2. Empirical Distribution
Using actual data to construct your own function for generation of data for your simulation

3. Empirical Distribution
Discrete or Continuous
Used when any random variable does not fit any known distribution
We use the cumulative distribution

4. Technique Take N observations Order values: x1 < x2 < .. < xN
Determine yn = n/N for n=1, 2,…,N
Plot points (xi, yi)
Connect points to obtain F(x)

5. Empirical Example Assume 10 observations:
1, 1, 2, 2, 4, 6, 7, 9, 10, 3 n X Yn

6. Example: Graph
1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1

7. Now What? If Discrete Values: Generate random values from 1 to 10
1,2  1 3,4  2
5   4
7   7
9   10
*Note that this is a very small example