I would like to create a function in order to integrate the product of 2 distributions (a PDF and CDF) with respect to x. This is in order to perform a probabilistic risk assessment and determine an 'expected total risk'.
My code I have so far, which does not work, is...
F <- function(x) {dgamma(x, shape=0.4259325, rate=8.1490741)*plnorm(x, meanlog=3.4906738, sdlog=0.2938556)}
c <- integrate( F, lower = 0, upper = inf)
Where and what have I done wrong here?
Additionally, Ive fitted my distributions using 'fitdist' function and for now am hard coding the distribution parameters to try and get the integration above working. However, how would I take the shape/rate/meanlog etc directly from the fitted distribution - the 'Fitted' object in the example code below?
x_vect <- seq(0.1,10, length.out = 1e3)
example <- rgamma(x_vect, shape=0.4259325, rate=8.1490741)
plot(x_vect, example, type = "l", log="x")
Fitted <- fitdist(example, "gamma")
plot(Fitted)