defmodule Distribution.Bernoulli do

  # Copyright 2019 Pieter Rijken
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.

  @moduledoc """
  Provides the Bernoulli distribution.
  """

  @enforce_keys [:pars]
  defstruct [:pars]
  
  @type t() :: %__MODULE__{
  }

end

defimpl Distribution, for: Distribution.Bernoulli do
  import Distribution.Bernoulli
  alias Distribution.Bernoulli

  @spec bernoulli(value :: number) :: ((...) -> number)
  defp bernoulli(value) when is_number(value) do
   fn () ->
       u = :rand.uniform()
       if u <= value, do: 1, else: 0
   end
  end
  
  def skewness(%Bernoulli{pars: [p]}), do: fn _ -> (1-2*p)/:math.sqrt(p*(1.0-p)) end
  def kurtosis(%Bernoulli{pars: [p]}), do: fn _ -> (1-6*p*(1.0-p))/p/(1.0-p) end
  def size(%Bernoulli{}), do: 1
  
  def cdf(%Bernoulli{}), do: raise Distribution.FunctionNotSupportedError, message: "cdf is not supported for the Constant distribution"
  def pdf(%Bernoulli{}), do: raise Distribution.FunctionNotSupportedError, message: "pdf is not supported for the Constant distribution"
  def random(%Bernoulli{pars: [value]}), do: bernoulli(value).()
  
end