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chi2fit

2.1.3
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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.

Retired package: Release invalid - Does not build and run properly
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chi2fit lib distributions exponential.ex
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lib/distributions/exponential.ex 

defmodule Chi2fit.Distribution.Exponential 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 """

  The exponential distribution.

  """



  defstruct [:pars, name: "exponential"]



  @type t() :: %__MODULE__{

    pars: [number()] | nil,

    name: String.t

  }



end



defimpl Chi2fit.Distribution, for: Chi2fit.Distribution.Exponential do

  alias Chi2fit.Distribution, as: D



  import D.Exponential

  alias D.Exponential



  defp exponential([avg: average]) do

    fn ->

      u = :rand.uniform()

      -average*:math.log(u)

    end

  end

  defp exponential(rate), do: exponential([avg: 1.0/rate])

  defp exponentialCDF(rate) when rate >= 0.0, do: fn t -> 1.0 - :math.exp(-rate*t) end

  defp exponentialCDF(rate) when rate < 0.0, do: fn _t -> 0.0 end



  def skewness(%Exponential{pars: nil}), do: fn _ -> 2 end

  def kurtosis(%Exponential{pars: nil}), do: fn _ -> 6 end

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



  def cdf(%Exponential{pars: nil}), do: fn x, [lambda] -> exponentialCDF(lambda).(x) end

  def cdf(%Exponential{pars: [lambda]}), do: fn x -> exponentialCDF(lambda).(x) end



  def pdf(%Exponential{pars: nil}), do: fn x, [lambda] -> lambda * :math.exp( -lambda*x ) end



  def random(%Exponential{pars: [lambda]}), do: exponential(lambda).()

  def random(%Exponential{pars: nil}), do: fn [lambda] -> exponential(lambda).() end



  def name(model), do: model.name



end



defimpl Inspect, for: Chi2fit.Distribution.Exponential do

  import Inspect.Algebra



  def inspect(dict, opts) do

    case dict.pars do

      nil ->

        "#Exponential<>"

      [rate] ->

        concat ["#Exponential<", to_doc("rate=#{rate}", opts), ">"]

      list ->

        concat ["#Exponential<", to_doc(list, opts), ">"]

    end

  end



end