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chi2fit

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Provides functions for fast matrix inversion, creation of empirical CDF from sample data including handling of asymmetric errors, and fitting to a funtion using chi-squared. The fitting procedure return the full covariance matrix describing the fitted parameters.

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chi2fit lib distributions dice.ex
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lib/distributions/dice.ex 

defmodule Distribution.Dice 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 Dice distribution.

  """



  defstruct [mode: :regular]

  

  @type t() :: %__MODULE__{

    mode: :regular | :gk4

  }



end



defimpl Distribution, for: Distribution.Dice do

  import Distribution.Dice

  alias Distribution.Dice



  @spec dice([] | number) :: ((...) -> number)

  defp dice([]), do: dice(1.0)

  defp dice([avg: avg]), do: dice(avg)

  defp dice(avg), do: %Distribution.Uniform{list: [avg*1,avg*2,avg*3,avg*4,avg*5,avg*6]}



  @spec dice_gk4([] | number) :: ((...) -> number)

  defp dice_gk4([]), do: dice_gk4(1.0)

  defp dice_gk4([avg: avg]), do: dice_gk4(avg)

  defp dice_gk4(avg), do: %Distribution.Uniform{list: [avg*3,avg*4,avg*4,avg*5,avg*5,avg*6]}



  def skewness(%Dice{}), do: raise Distribution.FunctionNotSupportedError, message: "skewness is not supported for the Dice distribution"

  def kurtosis(%Dice{}), do: raise Distribution.FunctionNotSupportedError, message: "kurtosis is not supported for the Dice distribution"

  def size(%Dice{}), do: 0



  def cdf(%Dice{}), do: raise Distribution.FunctionNotSupportedError, message: "cdf is not supported for the Dice distribution"

  def pdf(%Dice{}), do: raise Distribution.FunctionNotSupportedError, message: "pdf is not supported for the Dice distribution"



  def random(%Dice{mode: :regular}), do: dice([]).()

  def random(%Dice{mode: :gk4}), do: dice_gk4([]).()

  

end