newtons method - Use inverse CDF to generate random variable in R -


First of all, I have no idea, Professor gave a wrong question. Anyway, I tried to generate F (x) ~ U (0,1) , where CDF F (x) = 1- (1 + x) exp (-x) (For this CDF, you could not calculate with x = g (f)) hand.

Because 0 To INF

/ code>, uniroot () is out of the question therefore , I use the Newton method to write one.

Then, my code is such: 

  f = function (x) {ifelse (x> = 0 , X * f (-x), 0)} in.C = function (n) {a = runif (n) g = for tap (i in 1: n) {del = 1 x = 2 while (abs ( Del) & gt 1e-12) {del = (1- (1 + x) * exp (-x) -a [i]) / f (x) x = x-del} g [i] = x} g} system however, if  f (x)  is too small , And Newton is a step in the method, then there will be errors if the time (tt>   
 the result may be less than zero. Your code has been modified like this:  
  f = function (x) {ifelse (x> = 0, x * exp (-x), 0)} in.C = function AB (Dell) & gt; 1e-12) {if (x> = 0) {del = 1x = 2 for (i in 1: n) {del = 1x = 2} {a = runif (n) g = (1- (1 + x) * exp (-x) -a [i]) / f (x) x = x-del} second break if (x> gt = 0) g [i] = x} g [! Is.na (G)]} system.time (tt> lt; -c (100000) hist (tt, breaks = 70, right = F, freq = F), curve (f (x), = 0,   
 Obviously, the code is wrong, because I rejected the result of zero.  
 So, my guess is to calculate my code properly If not, then there is another way to do this. Any gratitude is appreciated.   
 
 
 You can    uniroot (.. ..)  for it.  
 [note: y The issue of this practice is to implement its version of Newton Rafsan technique, then tell me and I will remove the answer.]  
 If I understand it correctly, then you can see the density of the function with the possibility <  
  f = x * exp (-x) F = 1 - (1 + x) * exp (-x)   
 As you say, it can be from  U [0,1]  Generate Random Samples And  replaced by CDF inverse of F . The process is similar to those that have been posted, and except that you already have an expression for CDF.  
  f < - function (x) x * exp (-x) F & lt; - Function (X) 1- (1 + x) * Exp (-x) F.inv & lt; - Function (y) {uniroot (function (x) {f (x) -y}, interval = c (0,100)) $ root} F.inv & lt; - Vectorize (F.inv) x & lt; - seq (0, 10, length = 1000) y & lt; - seq (0,1, length = 1000) equal to (plot (x, f), type = "l", main = (x), plus (x, f), type = "l", main = "F" ("F"), type = "L", main = "F (x) inverted CDF")  / Pre> 
   
 Then,  X ~ U [0, 1]  and  Z = F.inv (X) .  
  set.seed (1) x <- runif (1000, 0,1) # Random sample from URL [0,1] Z

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