Random Variation in a Model

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 $c_1=0$ .