Continuous
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Continuous

The Empirical option under the Data Driven option of a Numeric Source block requires the following input data:

  • Data Name: The location of the SAS data set or JMP table that contains the data to be used to specify a continuous empirical distribution.

  • X : Name of the column in the data set that corresponds to the set of $n$ ordered values $x_1, x_2, ..., x_ n$.

  • C : Name of the column in the data set that corresponds to the cumulative probability values $c_1, c_2, ..., c_ n$ so that $0 \leq c_ j \leq 1$ for $j=1,2,...,n$; $c_ j < c_{j+1}$ for $j=1,2,...,n-1$; and $c_ n=1$.

The probability density function is defined as

\[ f(x) = \left\{ \begin{array}{ll} c_1 & \mbox{if\ } x=x_1 \\ c_ j - c_{j-1} & \mbox{if\ } x_{j-1} \leq x < x_ j, j=2,3,...,n \\ 0 & \mbox{if\ } x < x_1 \ \mbox{or\ } x \geq x_ n \end{array} \right. \]

If $c_1 > 0$, then the result is a mixed continuous-discrete distribution that returns $x_1$ with probability $c_1$ and with probability $1-c_1$ a continuous random variate on $(x_1,x_ n]$ using linear interpolation. If a true continuous distribution on $[x_1,x_ n]$ is desired, then specify $c_1=0$.

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