[R] combining distributions

[Ben Bolker]

Rachel Taylor-2 wrote:
> 
> 
> Hi all,
>  
> I am trying to generate a series of random numbers.  What I want to do is
> create n random Poisson numbers (easily done with the rpois function) and
> then use those generated numbers as the number of genenerated from another
> distribution (in this case, a function for the bounded Pareto distribution
> I have created).
>  
> Or, to put it in a less convoluted way, say rpois generates the values
> 40,35,32,28,46.  I then want to use my Pareto random number generator to
> generate 40, 35, 32, etc... numbers.  My prefered final output will be a
> vector with 1000 values, each value being the sum of (random poisson)
> pareto random numbers.  
>  

 I think this works:

rboundpareto <- function(n,gamma=0.7,alpha=5000000,beta=10000000000)
{
  U <- runif(n)
  A <- U*beta^gamma
  B <- U*alpha^gamma
  C <- beta^gamma
  Num <- -(A-B-C)
  D <- alpha^gamma
  E <- beta^gamma
  Denom <- D*E
  Frac <- Num/Denom
  Power <- -(1/gamma)
  Val <- Frac^Power
  Val
}

pp <- rpois(1000,20)
bb <- rboundpareto(sum(pp))
tapply(bb,rep(1:1000,pp),sum)

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