Empirical Distributions

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

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

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)

Empirical Example Assume 10 observations: 1, 1, 2, 2, 4, 6, 7, 9, 10, 3 n 1 2 3 4 5 6 7 8 9 10 X 1 1 2 2 3 4 6 7 9 10 Yn .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

Example: Graph 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 1 2 3 4 5 6 7 8 9 10

Now What? If Discrete Values: Generate random values from 1 to 10 1,2  1 3,4  2 5  3 6  4 7  6 8  7 9  9 10  10 *Note that this is a very small example