Example: Monte Carlo Simulation with a Custom Distribution Function

Functions > Design of Experiments > Monte Carlo Simulation > Example: Monte Carlo Simulation with a Custom Distribution Function

This example shows how to use a custom distribution function with the montecarlo function. Using custom distribution function enhances calculation speed, compared to using uniform distribution functions.

1. Create a custom distribution function that is based on the uniform distribution.

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    <define xmlns="http://schemas.mathsoft.com/math50">
      <function>
        <id labels="VARIABLE" xml:space="preserve">CustomDist</id>
        <boundVars>
          <id labels="VARIABLE" xml:space="preserve">n</id>
        </boundVars>
      </function>
      <program>
        <if>
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            <apply>
              <equal />
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id>
              <real>1</real>
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          </test>
          <then>
            <program>
              <apply>
                <indexer />
                <apply>
                  <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">runif</id>
                  <sequence>
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id>
                    <real>-0.01</real>
                    <real>0.01</real>
                  </sequence>
                </apply>
                <id labels="SYSTEM" xml:space="preserve" label-is-contextual="true">ORIGIN</id>
              </apply>
            </program>
          </then>
          <else>
            <program>
              <apply>
                <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">runif</id>
                <sequence>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id>
                  <real>-0.01</real>
                  <real>0.01</real>
                </sequence>
              </apply>
            </program>
          </else>
        </if>
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    </define>
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2. Define a function to simulate.

3. Define the numbers of samples to generate.

4. Call montecarlo to generate the samples.

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        <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">montecarlo</id>
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          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">F</id>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">N</id>
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            <str xml:space="preserve">Input</str>
            <real>0</real>
            <real>1</real>
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          <matrix rows="1" cols="1">
            <id labels="VARIABLE" xml:space="preserve">CustomDist</id>
          </matrix>
          <matrix rows="1" cols="2">
            <real>-0.01</real>
            <real>0.01</real>
          </matrix>
        </sequence>
      </apply>
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