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)Rate parameter \(\lambda\).
cut-off value.
point up to which to sum the distribution for the approximation.
logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.
probability.
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] 3
varPois(lambda = 3)
#> [1] 3
expValTruncPois(d = 0, lambda = 2, k0 = 2E2, less.than.d = FALSE)
#> This is an approximation
#> [1] 2
expValTruncPois(d = 2, lambda = 2, k0 = 2E2, less.than.d = TRUE)
#> This is an approximation
#> [1] 0.8120117
TVatRPois(kap = 0.8, lambda = 3, k0 = 2E2)
#> This is an approximation
#> [1] 5.596787
mgfPois(t = 1, lambda = 3)
#> [1] 173.269
pgfPois(t = 1, lambda = 3)
#> [1] 1