defmodule Wizard.Stats do
  @moduledoc """
  Wizard's Statistics functions
  """
  @doc """
  mean(list) - produces the mean from a list of numbers
  """
  @spec mean(list) :: number
  def mean(list) do
    Math.sum(list)/length list
  end

  @doc """
  binomial(n,theta) - produces a binomial distribution function with n items and
  theta success
  """
  @spec binomial(non_neg_integer, number) :: fun
  def binomial(n, theta) do
    fn x ->
      Math.combination(n, x) * Math.pow(theta, x) * Math.pow(1-theta, n-x)
    end
  end

  @doc """
  poisson(theta) - produces a poisson distribution function with probability theta
  """
  @spec poisson(number) :: fun
  def poisson(theta) do
    fn x ->
      (Math.pow(theta, x) * 1/Math.pow(Math.e, theta))/Math.factorial(x)
    end
  end
end