\(\text{PoissonVariate}\)

You can use the \(\text{PoissonVariate}\) function to calculate one or more random variates in a Poisson distribution.

You can use the \poissonv backslash command to insert this function.

The following variants of this function are available:

  • \(\text{integer } \text{PoissonVariate} \left ( \text{<}\lambda\text{>} \right )\)

  • \(\text{integer matrix } \text{PoissonVariate} \left ( \text{<number rows>}, \text{<number columns>}, \text{<}\lambda\text{>} \right )\)

Where \(\lambda\) is a scalar value representing the rate. The function is defined over \(\lambda > 0\) and will generate a runtime error, return NaN, or a matrix of NaN for values for which the function is not defined.

The single parameter version of this function will return a single random variate in a Poisson distribution. The three parameter version will return a matrix of random variates.

Note that this function is defined over the range \(\gamma > 0\) and will generate a runtime error, return NaN or a matrix of NaN for all other values.

The three parameter version, which includes \(\text{<number rows>}\) and \(\text{<number columns>}\) fields, returns an real matrix returning random deviates. The two parameter version returns a single value.

This function calculate random variates using transformation method based on the definition of the Cauchy-Lorentz quantile function:

The \(\text{PoissonVariate}\) function uses Knuth’s algorithm [6] for cases where \(\lambda \leq 12\). For values greater than 12, the \(\text{PoissonVariate}\) uses a proprietary rejection method.

The Poisson distribution models the the number of events over a given time time period caused by a memoryless process and, in this respect, is closely related to the exponential distribution that models time between events assuming a memoryless process.

Figure 186 shows the basic use of the \(\text{PoissonVariate}\) function.

../_images/poisson_variate_example.png

Figure 186 Example Use Of The PoissonVariate Function