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

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

MGFexponential(x, rate, deriv = 0)

Arguments

x

The value at which to evaluate the MGF

rate

The rate parameter value of the exponential distribution

deriv

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

Value

The number resulting from the function evaluation

Examples

# MGF of an exponential distribution, evaluated at -0.1:
MGFexponential(-0.1, rate = 0.05)
#> [1] 0.3333333
# Second moment of the distribution (second derivative evaluated at zero):
MGFexponential(0, rate = 0.05, deriv = 2)
#> [1] 800