Evaluate the moment generating function (MGF) of the gamma distribution or a derivative of the MGF

Evaluate the moment generating function (MGF) of the gamma distribution or a derivative of the MGF

MGFgamma(x, rate, shape, deriv = 0)

Arguments

x

The value at which to evaluate the MGF

rate

The rate parameter value of the gamma distribution

shape

The shape parameter values of the gamma distribution

deriv

An integer, the number of derivatives of the MGF to apply

Value

The number resulting from the function evaluation

Examples

# MGF of a gamma distributions, evaluated at -0.1:
MGFgamma(-0.1, rate = 0.7, shape = 3)
#> [1] 0.6699219
# Second moment of the distribution (second derivative evaluated at zero):
MGFgamma(0, rate = 0.7, shape = 3, deriv = 2)
#> [1] 24.4898