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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 bernoulli.ex
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lib/distributions/bernoulli.ex 

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