The sum of variables with this distribution itself follows this distribu- tion; that result is its reproductive property.
Inter-event times for this distribution follow the exponential distribution, and its moment-generating function is proportional to e to the t, quantity minus one. The sum of variables with this distribution itself follows this distribu- tion; that result is its reproductive property. This distribution applies when the question of how many events have not occurred has no meaning, and when the product of the number of trials with the probability remains fixed as the number of trials goes to infinity, it approximates the binomial distribution; that approximation is good for many trials with small probability of success. Its mean and variance are both equal to its single parameter, and its mass function at x for a parameter mu is e to the minus mu times mu to the x, over x factorial. Name this distribution used to model waiting times for arrivals, named for a Frenchman.
Inter-event times for this distribution follow the exponential distribution, and its moment-generating function is proportional to e to the t, quantity minus one.
{Poisson} distribution [accept {Poisson processes}]