Poisson distribution Measures

Calculates probability mass function (PMF), mean, variance, mode, standard deviation, kurtosis and skewness of a Poisson distribution.

X is a random variable following a Poisson distribution of parameter `lambda`.

Probability Mass Function (PMF)

`P(X = k) = (lambda^k*e^(-k))/(k!)`

Mean (or Expected value)

`E(X) = lambda`

Standard deviation

`sigma(X) = sqrt(lambda)`


`V(X) = lambda`


`S(X) = 1/sqrt(lambda)`


`K(X) = 1/lambda`


If `lambda` is not an integer,

`\text{mode}(X) = |__lambda__|`
`|__lambda__|` is the integer part of `lambda`.
If lambda is an integer, then variable X has two modes,
`\text{mode}(X) = lambda-1 \text{ and } lambda`

See also

Poisson distribution probabilities
Inverse Poisson distribution
Poisson distribution Chart
Statistics Calculators