[PYTHON] Probability distribution followed by differences between independent random variables that follow a Poisson distribution

Poisson distribution

When the random variable X satisfies $ P (X = k) = \ frac {\ lambda ^ ke ^ {-\ lambda}} {k!} $, it follows the Poisson distribution. The probability mass function of the Poisson distribution is shown below when $ \ lambda = 3 ... 10 $ is illustrated.

Two Poisson distributions

Prepare two columns that follow the Poisson distribution with $ \ lambda = 5 $.

poisson1 = np.random.poisson(lam=5, size=10000)
poisson2 = np.random.poisson(lam=5, size=10000)

Difference in probability distribution

diff = poisson2 - poisson1

Illustrated

It looks like it follows a normal distribution as above.

This is one of the distributions called Skellam distribution.