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