# $$\text{PoissonVariate}$$¶

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  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. Figure 186 Example Use Of The PoissonVariate Function