! SPDX-FileCopyrightText: 2022-2026 Jason Christopherson ! SPDX-License-Identifier: MIT ! ! MIT License ! ! Copyright (c) 2022-2026 Jason Christopherson ! ! Permission is hereby granted, free of charge, to any person obtaining a copy ! of this software and associated documentation files (the "Software"), to deal ! in the Software without restriction, including without limitation the rights ! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell ! copies of the Software, and to permit persons to whom the Software is ! furnished to do so, subject to the following conditions: ! ! The above copyright notice and this permission notice shall be included in all ! copies or substantial portions of the Software. ! ! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR ! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, ! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE ! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER ! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, ! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE ! SOFTWARE. module fstats_chi_squared_distribution use iso_fortran_env use ieee_arithmetic use fstats_distributions, only : distribution, probability_log use fstats_special_functions implicit none private public :: chi_squared_distribution type, extends(distribution) :: chi_squared_distribution !! Defines a Chi-squared distribution. integer(int32) :: dof !! The number of degrees of freedom. contains procedure, public :: log_pdf => cs_log_pdf procedure, public :: survival => cs_survival procedure, public :: log_cdf => cs_log_cdf procedure, public :: log_survival => cs_log_survival procedure, public :: pdf => cs_pdf procedure, public :: cdf => cs_cdf procedure, public :: mean => cs_mean procedure, public :: median => cs_median procedure, public :: mode => cs_mode procedure, public :: variance => cs_variance procedure, public :: defined_range => cs_range procedure, public :: recenter => cs_recenter end type contains pure elemental function cs_pdf(this, x) result(rst) !! Computes the probability density function. !! !! The PDF for a Chi-squared distribution is given as !! $$ f(x) = \frac{x^{k/2 - 1} \exp{-x / 2}} {2^{k / 2} !! \Gamma \left( \frac{k}{2} \right)} $$. class(chi_squared_distribution), intent(in) :: this !! The chi_squared_distribution object. real(real64), intent(in) :: x !! The value at which to evaluate the function. real(real64) :: rst !! The value of the function. ! Local Variables real(real64) :: arg ! Process arg = 0.5d0 * this%dof rst = exp(this%log_pdf(x)) end function pure elemental function cs_cdf(this, x) result(rst) !! Computes the cumulative distribution function. !! !! The CDF for a Chi-squared distribution is given as !! $$ F(x) = \frac{ \gamma \left( \frac{k}{2}, \frac{x}{2} \right) } !! { \Gamma \left( \frac{k}{2} \right)} $$. class(chi_squared_distribution), intent(in) :: this !! The chi_squared_distribution object. real(real64), intent(in) :: x !! The value at which to evaluate the function. real(real64) :: rst !! The value of the function. ! Local Variables real(real64) :: arg ! Process arg = 0.5d0 * this%dof rst = ieee_value(0.0d0, ieee_quiet_nan) if (this%dof <= 0 .or. ieee_is_nan(x)) return if (x <= 0.0d0) then rst = 0.0d0 else rst = regularized_gamma_lower(arg, 0.5d0 * x) end if end function pure function cs_mean(this) result(rst) !! Computes the mean of the distribution. class(chi_squared_distribution), intent(in) :: this !! The chi_squared_distribution object. real(real64) :: rst !! The mean. ! Process rst = real(this%dof, real64) end function pure function cs_median(this) result(rst) !! Computes the median of the distribution. class(chi_squared_distribution), intent(in) :: this !! The chi_squared_distribution object. real(real64) :: rst !! The median. ! Process rst = this%dof * (1.0d0 - 2.0d0 / (9.0d0 * this%dof))**3 end function pure function cs_mode(this) result(rst) !! Computes the mode of the distribution. class(chi_squared_distribution), intent(in) :: this !! The chi_squared_distribution object. real(real64) :: rst !! The mode. ! Process rst = max(this%dof - 2.0d0, 0.0d0) end function pure function cs_variance(this) result(rst) !! Computes the variance of the distribution. class(chi_squared_distribution), intent(in) :: this !! The chi_squared_distribution object. real(real64) :: rst !! The variance. ! Process rst = 2.0d0 * this%dof end function pure function cs_range(this) result(rst) !! Gets the defined range for the distribution. class(chi_squared_distribution), intent(in) :: this !! The chi_squared_distribution object. real(real64), dimension(2) :: rst !! The defined range of the probability distributions [0, infinity). As !! using a value of infinity may cause issue, this routine returns !! huge(0.0d0) instead. rst = [0.0d0, huge(0.0d0)] end function subroutine cs_recenter(this, x) !! Recenters the distribution about the supplied value. class(chi_squared_distribution), intent(inout) :: this !! The chi_squared_distribution object. real(real64), intent(in) :: x !! The value about which to recenter. ! Process this%dof = floor(x) end subroutine pure elemental function cs_log_pdf(this, x) result(rst) class(chi_squared_distribution), intent(in) :: this !! Distribution with valid parameters. real(real64), intent(in) :: x !! Evaluation point; discrete masses require integer-valued x. real(real64) :: rst !! Log density; outside support gives -infinity, invalid inputs give NaN. !! An integrable density singularity at a support endpoint gives +infinity. real(real64) :: first rst = ieee_value(0.0d0, ieee_quiet_nan) if (ieee_is_nan(x)) return if (this%dof <= 0) return rst = ieee_value(0.0d0, ieee_negative_inf) if (x < 0.0d0 .or. .not.ieee_is_finite(x)) return first = 0.5d0 * real(this%dof, real64) if (x == 0.0d0) then if (first < 1.0d0) rst = ieee_value(0.0d0, ieee_positive_inf) if (first == 1.0d0) rst = -log(2.0d0) return end if rst = (first - 1.0d0) * log(x) - 0.5d0 * x - first * log(2.0d0) - log_gamma(first) end function pure elemental function cs_survival(this, x) result(rst) class(chi_squared_distribution), intent(in) :: this !! Distribution with valid parameters. real(real64), intent(in) :: x !! Evaluation point; discrete tails include masses strictly above x. real(real64) :: rst !! Probability on [0, 1]; invalid parameters or NaN x give NaN. rst = ieee_value(0.0d0, ieee_quiet_nan) if (ieee_is_nan(x)) return if (this%dof <= 0) return rst = 1.0d0 if (x <= 0.0d0) return rst = regularized_gamma_upper(0.5d0 * real(this%dof, real64), 0.5d0 * x) end function pure elemental function cs_log_cdf(this, x) result(rst) class(chi_squared_distribution), intent(in) :: this !! Distribution with valid parameters. real(real64), intent(in) :: x !! Evaluation point. real(real64) :: rst !! Log probability; zero probability gives -infinity, invalid inputs NaN. rst = probability_log(this%cdf(x)) if (ieee_is_nan(rst)) return if (x > 0.0d0) rst = log_regularized_gamma_lower(0.5d0 * real(this%dof, real64), 0.5d0 * x) end function pure elemental function cs_log_survival(this, x) result(rst) class(chi_squared_distribution), intent(in) :: this !! Distribution with valid parameters. real(real64), intent(in) :: x !! Evaluation point. real(real64) :: rst !! Log probability; zero probability gives -infinity, invalid inputs NaN. rst = probability_log(this%survival(x)) if (ieee_is_nan(rst)) return if (x > 0.0d0) rst = log_regularized_gamma_upper(0.5d0 * real(this%dof, real64), 0.5d0 * x) end function end module fstats_chi_squared_distribution