 The probability distribution for poisson processes with constant rate λ per time interval is given by the following equation.formula_10

Defining formula_11 as the number of events that occur in the time interval formula_12

formula_13

It can be shown that inter-arrival times for events is exponentially distributed with a cumulative distribution function(CDF) of formula_14.The inverse of the exponential CDF is given by

formula_15

where formula_16 is an formula_17 uniformly distributed random variable.