! 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_log_normal_distribution use iso_fortran_env use ieee_arithmetic use fstats_distributions, only : distribution, probability_log use fstats_special_functions use fstats_normal_distribution, only : normal_distribution implicit none private public :: log_normal_distribution type, extends(distribution) :: log_normal_distribution !! Defines a normal distribution. real(real64) :: standard_deviation !! The standard deviation of the distribution. real(real64) :: mean_value !! The mean value of the distribution. contains procedure, public :: pdf => lnd_pdf procedure, public :: cdf => lnd_cdf procedure, public :: log_pdf => lnd_log_pdf procedure, public :: survival => lnd_survival procedure, public :: log_cdf => lnd_log_cdf procedure, public :: log_survival => lnd_log_survival procedure, public :: mean => lnd_mean procedure, public :: median => lnd_median procedure, public :: mode => lnd_mode procedure, public :: variance => lnd_variance procedure, public :: defined_range => lnd_range procedure, public :: recenter => lnd_recenter end type contains pure elemental function lnd_log_pdf(this, x) result(rst) !! Computes a log-normal log density from the underlying normal log density. class(log_normal_distribution), intent(in) :: this !! Law with finite log-mean and finite, positive log-standard deviation. real(real64), intent(in) :: x !! Evaluation point in observation space, not log space. real(real64) :: rst !! Log density; x <= 0 gives -infinity, invalid parameters or NaN x NaN. type(normal_distribution) :: normal normal%mean_value = this%mean_value normal%standard_deviation = this%standard_deviation rst = normal%log_pdf(0.0d0) if (ieee_is_nan(rst) .or. ieee_is_nan(x)) then rst = ieee_value(0.0d0, ieee_quiet_nan) return end if if (x <= 0.0d0 .or. .not.ieee_is_finite(x)) then rst = ieee_value(0.0d0, ieee_negative_inf) else rst = normal%log_pdf(log(x)) - log(x) end if end function pure elemental function lnd_survival(this, x) result(rst) !! Computes the log-normal upper-tail probability P(X > x). class(log_normal_distribution), intent(in) :: this !! Law with finite log-mean and finite, positive log-standard deviation. real(real64), intent(in) :: x !! Evaluation point in observation space. real(real64) :: rst !! Survival probability; x <= 0 gives one, invalid inputs give NaN. rst = exp(this%log_survival(x)) end function pure elemental function lnd_log_cdf(this, x) result(rst) !! Computes the log-normal log lower tail using the normal log-CDF. class(log_normal_distribution), intent(in) :: this !! Law with finite log-mean and finite, positive log-standard deviation. real(real64), intent(in) :: x !! Evaluation point in observation space. real(real64) :: rst !! Log CDF; x <= 0 gives -infinity, invalid inputs give NaN. type(normal_distribution) :: normal normal%mean_value = this%mean_value normal%standard_deviation = this%standard_deviation rst = normal%log_cdf(0.0d0) if (ieee_is_nan(rst) .or. ieee_is_nan(x)) then rst = ieee_value(0.0d0, ieee_quiet_nan) else if (x <= 0.0d0) then rst = ieee_value(0.0d0, ieee_negative_inf) else rst = normal%log_cdf(log(x)) end if end function pure elemental function lnd_log_survival(this, x) result(rst) !! Computes the log-normal log upper tail using the normal log-survival. class(log_normal_distribution), intent(in) :: this !! Law with finite log-mean and finite, positive log-standard deviation. real(real64), intent(in) :: x !! Evaluation point in observation space. real(real64) :: rst !! Log survival probability; x <= 0 gives zero, invalid inputs give NaN. type(normal_distribution) :: normal normal%mean_value = this%mean_value normal%standard_deviation = this%standard_deviation rst = normal%log_survival(0.0d0) if (ieee_is_nan(rst) .or. ieee_is_nan(x)) then rst = ieee_value(0.0d0, ieee_quiet_nan) else if (x <= 0.0d0) then rst = 0.0d0 else rst = normal%log_survival(log(x)) end if end function pure elemental function lnd_pdf(this, x) result(rst) !! Computes the probability density function. !! !! The PDF for a log-normal distribution is given as !! $$ f(x) = \frac{1}{x \sigma \sqrt{2 \pi}} \exp{\left(- \frac{\left( !! \ln{x} - \mu \right)^2}{2 \sigma^2} \right)} $$ class(log_normal_distribution), intent(in) :: this !! The log_normal_distribution object. real(real64), intent(in) :: x !! The value at which to evaluate the function. real(real64) :: rst !! The value of the function. rst = exp(this%log_pdf(x)) end function pure elemental function lnd_cdf(this, x) result(rst) !! Computes the cumulative distribution function. !! !! The CDF for a log-normal distribution is given as !! $$ F(x) = \frac{1}{2} \left(1 + erf\left( \frac{\ln{x} - \mu} !! {\sigma \sqrt{2}} \right) \right) $$ class(log_normal_distribution), intent(in) :: this !! The log_normal_distribution object. real(real64), intent(in) :: x !! The value at which to evaluate the function. real(real64) :: rst !! The value of the function. rst = exp(this%log_cdf(x)) end function pure function lnd_mean(this) result(rst) !! Computes the mean of the distribution class(log_normal_distribution), intent(in) :: this !! The log_normal distribution object. real(real64) :: rst !! The mean rst = exp(this%mean_value + 0.5d0 * this%standard_deviation**2) end function pure function lnd_median(this) result(rst) !! Computes the median of the distribution class(log_normal_distribution), intent(in) :: this !! The log_normal distribution object. real(real64) :: rst !! The median rst = exp(this%mean_value) end function pure function lnd_mode(this) result(rst) !! Computes the mode of the distribution class(log_normal_distribution), intent(in) :: this !! The log_normal distribution object. real(real64) :: rst !! The mode rst = exp(this%mean_value - this%standard_deviation**2) end function pure function lnd_variance(this) result(rst) !! Computes the variance of the distribution class(log_normal_distribution), intent(in) :: this !! The log_normal distribution object. real(real64) :: rst !! The variance rst = stable_expm1(this%standard_deviation**2) * & exp(2.0d0 * this%mean_value + this%standard_deviation**2) end function pure function lnd_range(this) result(rst) !! Gets the defined range for the distribution. class(log_normal_distribution), intent(in) :: this !! The log_normal_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 lnd_recenter(this, x) !! Recenters the distribution about the supplied value. class(log_normal_distribution), intent(inout) :: this !! The log_normal_distribution object. real(real64), intent(in) :: x !! The value about which to recenter. this%mean_value = x end subroutine end module fstats_log_normal_distribution