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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 uniform.ex
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lib/distributions/uniform.ex 

defmodule Distribution.Uniform 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 Uniform distribution.

  """



  defstruct [:pars]

  

  @type t() :: %__MODULE__{

    pars: [number()] | {number,number}

  }



end



defimpl Distribution, for: Distribution.Uniform do

  import Distribution.Uniform

  alias Distribution.Uniform



  @spec uniform(Keyword.t) :: ((...) -> number)

  defp uniform([]), do: uniform(0, 2.0)

  defp uniform([avg: average]), do: uniform(0,2*average)

  defp uniform(list) when is_list(list), do: fn () -> Enum.random(list) end

  defp uniform(range = %Range{}), do: fn () -> Enum.random(range) end



  @spec uniform(min::integer(),max::integer()) :: ((...) -> number)

  defp uniform(min,max) when max>=min, do: fn () -> random(min,max) end



  @spec random(min::number(),max::number()) :: number()

  defp random(min,max) when max >= min do

    min + (max-min)*:rand.uniform()

  end



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

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

  def size(%Uniform{}), do: 1



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

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



  @doc """

  ## Examples:



      iex> :rand.seed :exsplus, {101, 102, 103}

      iex> random %Distribution.Uniform{pars: {0,20}}

      14.897380811651171

      iex> random %Distribution.Uniform{pars: 0..20}

      11

      iex> random %Distribution.Uniform{pars: [1,2,3,4,5]}

      1



  """

  def random(%Uniform{pars: {min,max}}), do: uniform(min,max).()

  def random(%Uniform{pars: r=%Range{}}), do: uniform(r).()

  def random(%Uniform{pars: list}), do: uniform(list).()

  def random(%Uniform{}), do: uniform([]).()

  

end