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Empirical Distributions

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.

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Empirical Distributions

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  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 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

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

  7. 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

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