Distributacalcul (version 0.2.2)

PGF_pois: Probability Generating Function of the Poisson distribution

Description

Probability Generating Function (PGF) of the Poisson distribution with rate parameter \(\lambda\).

Usage

PGF_pois(t, lambda)

Arguments

t

t

lambda

Rate parameter \(\lambda\).

Value

Function :

• MGF_pois gives the moment generating function (MGF).

• PGF_pois gives the probability generating function (PGF).

• E_pois gives the expected value.

• V_beta gives the variance.

• Etronq_pois gives the truncated mean.

• TVaR_pois gives the Tail Value-at-Risk.

Invalid parameter values will return an error detailing which parameter is problematic.

Details

The Poisson distribution with rate parameter \(\lambda\) has probability mass function : $$Pr(X = k) = \frac{\lambda^k \textrm{e}^{-\lambda}}{k!}$$ for \(k = 0, 1, 2, \dots\), and \(\lambda > 0\)

See Also

Other Poisson Distribution: E_pois(), Etronq_pois(), MGF_pois(), TVaR_pois(), V_pois()

Examples

# NOT RUN {
PGF_pois(t = 1, lambda = 3)

# }