Pois.Rd
Poisson distribution with rate parameter \(\lambda\).
expValPois(lambda) varPois(lambda) expValTruncPois(d, lambda, k0, less.than.d = TRUE) TVatRPois(kap, lambda, k0) mgfPois(t, lambda) pgfPois(t, lambda)
lambda | Rate parameter \(\lambda\). |
---|---|
d | cut-off value. |
k0 | point up to which to sum the distribution for the approximation. |
less.than.d | logical; if |
kap | probability. |
t | t. |
Function :
expValPois
gives the expected value.
varPois
gives the variance.
expValTruncPois
gives the truncated mean.
TVatRPois
gives the Tail Value-at-Risk.
mgfPois
gives the moment generating function (MGF).
pgfPois
gives the probability generating function (PGF).
Invalid parameter values will return an error detailing which parameter is problematic.
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 \(\lambda > 0\)
expValPois(lambda = 3)#> [1] 3varPois(lambda = 3)#> [1] 3expValTruncPois(d = 0, lambda = 2, k0 = 2E2, less.than.d = FALSE)#>#> [1] 2expValTruncPois(d = 2, lambda = 2, k0 = 2E2, less.than.d = TRUE)#>#> [1] 0.8120117TVatRPois(kap = 0.8, lambda = 3, k0 = 2E2)#>#> [1] 5.596787mgfPois(t = 1, lambda = 3)#> [1] 173.269pgfPois(t = 1, lambda = 3)#> [1] 1