[R] triangular PDF

[Andy Jacobson]

Howdy,

        I couldn't find any way to generate deviates from a triangular
        PDF in R, so here's a function to do so.

        -Andy

rtri <- function(n=1,min=0,max=1,ml=0.5) {

  # Return independent random deviates from a
  # triangular distribution.
  
  # n is number of deviates requested
  # min, max are lower and upper limits of r.v. range
  # ml is the most-likely value

  # if ml = (min+max)/2, pdf is symmetric
  # if ml=min, pdf is left triangular
  # if ml=max, pdf is right triangular

  # Method reference is Section 7.3.9 of Law and Keaton (1982):
  
  # @Book{law82a,
  #  author =	 {Averill M. Law and W. David Keaton},
  #  title = 	 {Simulation modeling and analysis},
  #  publisher = 	 {Mc{G}raw-Hill},
  #  year = 	 1982
  #}

  # Written by Andy Jacobson (andyj at splash.princeton.edu), 6 Dec 2002
  # Credit is also due to Jeffrey S. Smith, (jsmith at eng.auburn.edu),
  # whose C++ implementation I looked at first.

  if((ml<min)||(ml>max)) {
    stop("ml outside of range [min max]")
  }
  
  u <- runif(n)

  mode <- (ml-min)/(max-min)  # "mode" defined in range [0 1] (rescaling will be done last)

  s1 <- which(u<=mode)
  s2 <- which(u>mode)

  u[s1] <- sqrt(mode*u[s1])
  u[s2] <- 1-sqrt((1-mode)*(1-u[s2]))

  min+(max-min)*u
  
}


-- 
Andy Jacobson

arj at gfdl.gov

Program in Atmospheric and Oceanic Sciences
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Princeton University
PO Box CN710 Princeton, NJ 08544-0710 USA

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