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)`
Variance
`V(X) = lambda`
Skewness
`S(X) = 1/sqrt(lambda)`
Kurtosis
`K(X) = 1/lambda`
Mode
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