A ready-to-use CGF object for the Gamma distribution with shape \(\alpha\)
and rate \(\beta\). The parameter_vector used when calling methods such as K(tvec, parameter_vector)
should be a numeric vector \(c(\alpha, \beta)\).
Format
An object of class CGF (an R6 class), with the usual methods:
K, K1, K2, K3operator, K4operator, etc.
Details
CGF: For a Gamma random variable \(X\) with shape \(\alpha\) and rate \(\beta\), the cumulant generating function is: $$K(t;\alpha, \beta) = -\alpha \,\log \bigl(1 - t/\beta\bigr), \quad t < \beta.$$
Parameter Vector: The parameter_vector is assumed to have the form
\((\alpha, \beta)\). You must ensure
that \(t < \beta\) for valid evaluations.
Examples
# Evaluate K at t=0.5 for shape=2, rate=2 (thus t<2).
# param = c(2, 2)
GammaCGF$K(0.5, c(2,2))
#> [1] 0.5753641