pm_distPareto::getParetoLogQuan Interface Reference

Generate and return a scalar (or array of arbitrary rank) of the natural logarithm(s) of quantile corresponding to the specified CDF of (Truncated) Pareto distribution with parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\).
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Detailed Description

Generate and return a scalar (or array of arbitrary rank) of the natural logarithm(s) of quantile corresponding to the specified CDF of (Truncated) Pareto distribution with parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\).

See the documentation of pm_distPareto for more information on the quantile of the (Truncated) Pareto distribution.

Parameters

[in]	logCDF	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing the natural logarithm of the desired CDF value of the distribution corresponding to the output quantile.
[in]	alpha	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the shape parameter ( \(\alpha\)) of the distribution.
[in]	logMinX	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing the natural logarithm of the first scale parameter of the distribution, representing the minimum of the support of the distribution.
[in]	logMaxX	: The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing the natural logarithm of the second scale parameter of the distribution, representing the maximum of the support of the distribution. (optional, default = \(+\infty\))

Returns

logx : The output scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha, containing the natural logarithm of the quantile corresponding to the input logCDF.
By definition, the condition logMinX <= logx <= logMaxX holds.

Possible calling interfaces ⛓

use pm_distPareto, only: getParetoLogQuan
 
logx = getParetoLogQuan(logCDF, alpha, logMinX) ! Pareto distribution.
logx = getParetoLogQuan(logCDF, alpha, logMinX, logMaxX) ! Truncated Pareto distribution.
!

Warning

The condition alpha < 0 must hold for the corresponding input arguments.
The condition logCDF < 0 must hold for the corresponding input arguments.
The conditions logMinX < logMaxX must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

Remarks

The procedures under discussion are elemental.

See also

setParetoLogQuan

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_distPareto, only: getParetoLogQuan
    use pm_io, only: display_type
 
    implicit none
 
    real                    :: logx(3)
 
    type(display_type)      :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the Quantile Function of the Pareto distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("logx(1) = getParetoLogQuan(logCDF = -3., alpha = -2., logMinX = -2.) ! Pareto distribution.")
                    logx(1) = getParetoLogQuan(logCDF = -3., alpha = -2., logMinX = -2.) ! Pareto distribution.
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("logx(1:3) = getParetoLogQuan(logCDF = -[3., 4., 5.], alpha = -[+2., +3., +4.], logMinX = -2.) ! Pareto distribution.")
                    logx(1:3) = getParetoLogQuan(logCDF = -[3., 4., 5.], alpha = -[+2., +3., +4.], logMinX = -2.) ! Pareto distribution.
    call disp%show("logx(1:3)")
    call disp%show( logx(1:3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the Quantile Function of the Truncated Pareto distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("logx(1) = getParetoLogQuan(logCDF = -3., alpha = -1., logMinX = -2., logMaxX = 5.) ! Truncated Pareto distribution.")
                    logx(1) = getParetoLogQuan(logCDF = -3., alpha = -1., logMinX = -2., logMaxX = 5.) ! Truncated Pareto distribution.
    call disp%show("logx(1)")
    call disp%show( logx(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("logx(1:3) = getParetoLogQuan(logCDF = -[3., 1., 2.], alpha = -[+1., +2., +3.], logMinX = -2., logMaxX = 5.) ! Truncated Pareto distribution.")
                    logx(1:3) = getParetoLogQuan(logCDF = -[3., 1., 2.], alpha = -[+1., +2., +3.], logMinX = -2., logMaxX = 5.) ! Truncated Pareto distribution.
    call disp%show("logx(1:3)")
    call disp%show( logx(1:3) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_arraySpace, only: setLinSpace
        use pm_distPareto, only: getParetoLogCDF
        real :: alpha(2), logMinX, logMaxX, logx(4), logCDF(2000)
        integer(IK) :: fileUnit, i
        call setLinSpace(logCDF, x1 = log(.001), x2 = log(.999))
        alpha = -[+0.5, +2.0]
        logMinX = log(3.)
        logMaxX = log(8.)
        open(newunit = fileUnit, file = "getParetoLogQuan.RK.txt")
        do i = 1, size(logCDF, 1, IK)
            logx(1:2) = getParetoLogQuan(logCDF(i), alpha, logMinX)
            logx(3:4) = getParetoLogQuan(logCDF(i), alpha, logMinX, logMaxX)
            write(fileUnit, "(5(g0,:,', '))") exp(logCDF(i)), exp(logx(1:4))
        end do
        close(fileUnit)
    end block
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the Quantile Function of the Pareto distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
logx(1) = getParetoLogQuan(logCDF = -3., alpha = -2., logMinX = -2.) ! Pareto distribution.
logx(1)
-1.97446537
 
 
logx(1:3) = getParetoLogQuan(logCDF = -[3., 4., 5.], alpha = -[+2., +3., +4.], logMinX = -2.) ! Pareto distribution.
logx(1:3)
-1.97446537, -1.99383819, -1.99830985
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the Quantile Function of the Truncated Pareto distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
logx(1) = getParetoLogQuan(logCDF = -3., alpha = -1., logMinX = -2., logMaxX = 5.) ! Truncated Pareto distribution.
logx(1)
-1.94897854
 
 
logx(1:3) = getParetoLogQuan(logCDF = -[3., 1., 2.], alpha = -[+1., +2., +3.], logMinX = -2., logMaxX = 5.) ! Truncated Pareto distribution.
logx(1:3)
-1.94897854, -1.77066267, -1.95152891
 
 

Postprocessing of the example output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import glob
import sys
 
linewidth = 2
fontsize = 17
 
marker ={ "CK" : "-"
        , "IK" : "."
        , "RK" : "-"
        }
xlab =  { "CK" : "CDF ( real/imaginary components )"
        , "IK" : "CDF ( integer-valued )"
        , "RK" : "CDF ( real-valued )"
        }
legends =   [ r"$\alpha = -.5, x_{min} = +3., x_{max} = +\infty$"
            , r"$\alpha = -2., x_{min} = +3., x_{max} = +\infty$"
            , r"$\alpha = -.5, x_{min} = +3., x_{max} = +8$"
            , r"$\alpha = -2., x_{min} = +3., x_{max} = +8$"
            ]
 
for kind in ["IK", "CK", "RK"]:
 
    pattern = "*." + kind + ".txt"
    fileList = glob.glob(pattern)
    if len(fileList) == 1:
 
        df = pd.read_csv(fileList[0], delimiter = ", ")
 
        fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
        ax = plt.subplot()
 
        if kind == "CK":
            plt.plot( df.values[:, 0]
                    , df.values[:,1:5]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "r"
                    )
            plt.plot( df.values[:, 1]
                    , df.values[:,1:5]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "blue"
                    )
        else:
            plt.plot( df.values[:, 0]
                    , df.values[:,1:]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "r"
                    )
            ax.legend   ( legends
                        , fontsize = fontsize - 5
                        )
 
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        ax.set_xlabel(xlab[kind], fontsize = 17)
        ax.set_ylabel("Quantile Function", fontsize = 17)
        #ax.set_xscale("log")
        #ax.set_yscale("log")
        ax.set_ylim([3, 10])
 
        plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
        ax.tick_params(axis = "y", which = "minor")
        ax.tick_params(axis = "x", which = "minor")
 
        plt.tight_layout()
        plt.savefig(fileList[0].replace(".txt",".png"))
 
    elif len(fileList) > 1:
 
        sys.exit("Ambiguous file list exists.")

Visualization of the example output ⛓

Test:

test_pm_distPareto

Todo:

Very Low Priority: This generic interface can be extended to complex arguments.

Final Remarks ⛓

---

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For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
   

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 1358 of file pm_distPareto.F90.

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The documentation for this interface was generated from the following file:

• src/fortran/main/pm_distPareto.F90