Distributacalcul (version 0.2.2)

Etronq_pois: Truncated mean of the Poisson distribution

Description

Truncated mean of the Poisson distribution with rate parameter \(\lambda\).

Usage

Etronq_pois(d, lambda, k0, less.than.d = TRUE)

Arguments

d

cut-off value.

lambda

Rate parameter \(\lambda\).

k0

point up to which to sum the distribution to approximate the expected value.

less.than.d

logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.

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(), MGF_pois(), PGF_pois(), TVaR_pois(), V_pois()

Examples

# NOT RUN {
Etronq_pois(d = 0, lambda = 2, k0 = 2E2, less.than.d = FALSE)
Etronq_pois(d = 2, lambda = 2, k0 = 2E2, less.than.d = TRUE)

# }