Generating random variable from density function

Question

How can I generate a random variable of size n= 2914 if I have the density function?.

So the problem is that I have the density f(x) (function well defined)

P<-function(a,e) { ( (1/6)*(1^3) )-((a/2)*(1^2)) +(((((a)^2)/2)+e)*1)}

D<-function(u,mu,sigma) {dlogis(u,mu,sigma)}

K<- function(u,a,e) {(((1/2)*(u^2))- (a*u) +(((a^2)/2)+e))}

H<-function(u,mu,sigma){ plogis(u,mu,sigma, lower.tail = TRUE)}

Fprim<- function(u,a,e,mu,sigma) (1/P(a,e))*(D(u,mu,sigma))*(K(H(u,mu,sigma),a,e))

Fprim(1,a,e,mu,sigma) 

df<- function(u)  Fprim(u,a,e,mu,sigma)

#### Parameter n,a,e,mu,sigma 
n<-2914
mu<- -0.42155226
sigma<- 0.60665552
a<- 0.43218138
e<- 0.02149706

I think I need to reverse and to use Monte Carlo, I don't know how to do?

Answer 1

I suppose you mean

df <- function(u)  Fprim(u,a = 0.43218138, e = 0.02149706, mu = -0.42155226, sigma = 0.60665552)

I propose

 x <- seq(-20,20,length=10001)
 y <- df(x)
 y1 <- cumsum(y)*diff(x)[1]

 pf <- approxfun(x,y1)
 qf <- approxfun(y1,x)
 rf <- function(n) qf(runif(n))

The functions qf, pf and rf are the quantile, cdf, and random generator for the density df. So you just end by

rf(2914)