Support for other distribution, e.g. Normal, Poisson

[beloglazov]

It's just an enhancement suggestion: it would be nice to have support for other distributions in addition to the uniform distribution, such as the normal and Poisson distributions.

Thanks for you great work!

[beloglazov]

I'm trying to implement Knuth's algorithm for generating Poisson samples (http://en.wikipedia.org/wiki/Poisson_distribution#Generating_Poisson-distributed_random_variables) and came up with the following:

    def poissonSample(lambda: Double): Rng[Int] = {
      val L = math.exp(-lambda)

      @annotation.tailrec
      def loop(p: Double, k: Int): Rng[Int] = {          
        for {                                         
          u <- choosedouble(0, 1) 
        } yield {
          if (p > L) loop(p * u, k + 1)   
          else k 
        }         
      }                                             

      loop(1.0, 0).map(_ - 1)                        
    }

This doesn't compile, as the internal call to loop is expected to return Int instead of Rng[Int]. I'm really a beginner in functional programming, and can't figure out at the moment how to solve this. I'd be happy to get any suggestions. Thanks!

[etorreborre]

Try:

def poissonSample(lambda: Double): Rng[Int] = {
  val L = math.exp(-lambda)

  @annotation.tailrec
  def loop(p: Double, k: Int): Rng[Int] = {          
    choosedouble(0, 1).flatMap { u =>                                         
      if (p > L) loop(p * u, k + 1)   
      else       Rng.constant(k) 
    }         
  }                                             

  loop(1.0, 0).map(_ - 1)                        
}

[beloglazov]

Thanks! That fixed the type issue. However, loop is not tail-recursive:

[error] could not optimize @tailrec annotated method loop: it contains a recursive call not in tail position
[error]       choosedouble(0, 1).flatMap(u =>

Is there any way to make it tail-recursive?

[beloglazov]

If you are interested, here is an implementation of the Box-Muller method for generating normally distributed numbers:

def normalSample(mean: Double, variance: Double): Rng[Double] = {
  // Box–Muller method
  choosedouble(0, 1).fill(2) map { u =>
    val z = math.sqrt(-2 * math.log(u(0))) * math.cos(2 * math.Pi * u(1))
    mean + math.sqrt(variance) * z
  }
}

[markhibberd]

@beloglazov I don't think it needs to be tail recursive. Rng will take care of that for you internally.

[beloglazov]

@markhibberd Great, thanks for letting me know! I need to dig more into the Rng implementation to understand that.