Random Variation in a Model

Count-Based

A method described in Leemis (2004) is used for generating arrival times from an estimated NHPP. This method uses event-time data that are given as counts that occur in disjoint subintervals (as opposed to the event times themselves). For the NHPP Count option under the Data Driven option of a Numeric Source block, the following inputs are required as shown in Figure B.4:

Data Name: The location of the SAS data set or JMP table that contains the data to be used to estimate a cumulative intensity (rate) function.
X: Name of the column in the data set that specifies the subinterval cutoff points $x_0,x_1,...,x_ m$ so that the NHPP has an intensity function that is piecewise constant on each subinterval $(x_0,x_1],(x_1,x_2],...,(x_{m-1},x_ m]$ . The subintervals do not necessarily have equal widths. The NHPP is defined on the time interval $(0,S]$ so that $x_0=0$ , $x_ m=S$ , and m is the number of subintervals. The time units must be consistent with the data. For example, if the interval of interest is from 1:00 p.m. to 5:30 p.m., then the interval $(x_0,x_ m]$ is $(0,4.5]$ if the data are in hours or $(0,270]$ if the data are in minutes.
Counts: Name of the column in the data set where each value $c_1,c_2,...,c_ m$ is the total number of observed events in each subinterval over all replications. Specifically, $c_1$ is the total number of observed events in the subinterval $(x_0,x_1]$ . The length of the Counts column should be one less than the length of the X column.
Number of Replications: The number of realizations of the observed process.

Figure B.4: NHPP Count Option for the Numeric Source Block