pm_distGenGamma::setGenGammaCDF Interface Reference

Return the Cumulative Distribution Function (CDF) of the Generalized Gamma distribution for an input x within the support of the distribution \(x \in (0,+\infty)\). More...

Detailed Description

Return the Cumulative Distribution Function (CDF) of the Generalized Gamma distribution for an input x within the support of the distribution \(x \in (0,+\infty)\).

See the documentation of pm_distGenGamma for more information on the GenGamma CDF.

Parameters

[out]	cdf	: The output scalar or array of the same shape as any input array-like argument, of the same type and kind the input argument x, containing the CDF of the distribution at the specified x.
[in]	x	: The input scalar or array of the same shape as other array like arguments, of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the values at which the CDF must be computed.
[in]	kappa	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as x, containing the shape parameter of the distribution. (optional, default = 1.. It must be present if invOmega are also present.)
[in]	invOmega	: The input scalar or array of the same shape as other array-valued arguments, containing the inverse of the second shape parameter ( \(\omega\)) of the distribution. (optional, default = 1.)
[in]	invSigma	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as x, containing the rate (inverse scale) parameter of the distribution. (optional, default = 1.. It can be present only if all previous arguments are also present.)
[out]	info	: The output scalar of type integer of default kind IK. On output, it is set to positive the number of iterations taken for the series representation of the Gamma function to converge. If the algorithm fails to converge, then info is set to the negative of the number of iterations taken by the algorithm. An negative output value signifies the lack of convergence and failure to compute the CDF. This is likely to happen if the input value for kappa is too large.

Possible calling interfaces ⛓

use pm_distGenGamma, only: setGenGammaCDF
 
call setGenGammaCDF(cdf, x, info)
call setGenGammaCDF(cdf, x, kappa, info)
call setGenGammaCDF(cdf, x, kappa, invOmega, info)
call setGenGammaCDF(cdf, x, kappa, invOmega, invSigma, info)

Warning

The condition \(x \in (0,+\infty)\) must hold for the corresponding input arguments.
The condition invSigma > 0 must hold for the corresponding input arguments.
The condition invOmega > 0 must hold for the corresponding input arguments.
The condition kappa > 0 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

getGenGammaCDF

Example usage ⛓

program example
 
    use pm_kind, only: SK
    use pm_kind, only: IK, LK
    use pm_kind, only: RK => RKS ! all other real kinds are also supported.
    use pm_io, only: display_type
    use pm_arraySpace, only: getLinSpace
    use pm_arraySpace, only: getLogSpace
    use pm_distGenGamma, only: setGenGammaCDF
 
    implicit none
 
    integer(IK) , parameter     :: NP = 1000_IK
    real(RK)    , dimension(NP) :: point, cdf, kappa, invOmega, invSigma
    integer(IK)                 :: info(NP)
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    kappa = getLinSpace(+0.5_RK, +2._RK, count = NP)
    invOmega = getLogSpace(logx1 = log(0.1_RK), logx2 = log(10._RK), count = NP)
    invSigma = getLogSpace(-3._RK, +3._RK, count = NP)
    point = getLogSpace(log(.01_RK), log(+10._RK), count = NP)
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the Cumulative Distribution Function (CDF) of GenGamma distribution at the specified values.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the cdf at an input scalar real value.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("call setGenGammaCDF(cdf(1), 0.5_RK, info(1))")
                    call setGenGammaCDF(cdf(1), 0.5_RK, info(1))
    call disp%show("if (info(1) < 0) error stop 'The computation of the cdf info.'")
                    if (info(1) < 0) error stop 'The computation of the cdf info.'
    call disp%show("cdf(1)")
    call disp%show( cdf(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("kappa(1)")
    call disp%show( kappa(1) )
    call disp%show("call setGenGammaCDF(cdf(1), 0.5_RK, kappa(1), info(1))")
                    call setGenGammaCDF(cdf(1), 0.5_RK, kappa(1), info(1))
    call disp%show("if (info(1) < 0) error stop 'The computation of the cdf info.'")
                    if (info(1) < 0) error stop 'The computation of the cdf info.'
    call disp%show("cdf(1)")
    call disp%show( cdf(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("kappa(1)")
    call disp%show( kappa(1) )
    call disp%show("invOmega(1)")
    call disp%show( invOmega(1) )
    call disp%show("call setGenGammaCDF(cdf(1), 0.5_RK, kappa(1), invOmega(1), info(1))")
                    call setGenGammaCDF(cdf(1), 0.5_RK, kappa(1), invOmega(1), info(1))
    call disp%show("if (info(1) < 0) error stop 'The computation of the cdf info.'")
                    if (info(1) < 0) error stop 'The computation of the cdf info.'
    call disp%show("cdf(1)")
    call disp%show( cdf(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("kappa(1)")
    call disp%show( kappa(1) )
    call disp%show("invOmega(1)")
    call disp%show( invOmega(1) )
    call disp%show("call setGenGammaCDF(cdf(1), 0.5_RK, kappa(1), invOmega(1), invSigma(1), info(1))")
                    call setGenGammaCDF(cdf(1), 0.5_RK, kappa(1), invOmega(1), invSigma(1), info(1))
    call disp%show("if (info(1) < 0) error stop 'The computation of the cdf info.'")
                    if (info(1) < 0) error stop 'The computation of the cdf info.'
    call disp%show("cdf(1)")
    call disp%show( cdf(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the cdf at an input vector real value with different parameter values.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("kappa(1)")
    call disp%show( kappa(1) )
    call disp%show("call setGenGammaCDF(cdf(1:NP:NP/5), 0.5_RK, kappa(1:NP:NP/5), info(1:NP:NP/5))")
                    call setGenGammaCDF(cdf(1:NP:NP/5), 0.5_RK, kappa(1:NP:NP/5), info(1:NP:NP/5))
    call disp%show("if (info(1) < 0) error stop 'The computation of the cdf info.'")
                    if (info(1) < 0) error stop 'The computation of the cdf info.'
    call disp%show("cdf(1:NP:NP/5)")
    call disp%show( cdf(1:NP:NP/5) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("kappa(1)")
    call disp%show( kappa(1) )
    call disp%show("call setGenGammaCDF(cdf(1:NP:NP/5), point(1:NP:NP/5), kappa(1:NP:NP/5), info(1:NP:NP/5))")
                    call setGenGammaCDF(cdf(1:NP:NP/5), point(1:NP:NP/5), kappa(1:NP:NP/5), info(1:NP:NP/5))
    call disp%show("if (any(info(1:NP:NP/5) < 0)) error stop 'The computation of the cdf info.'")
                    if (any(info(1:NP:NP/5) < 0)) error stop 'The computation of the cdf info.'
    call disp%show("cdf(1:NP:NP/5)")
    call disp%show( cdf(1:NP:NP/5) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        integer     :: fileUnit, i
        real(RK)    :: cdf(NP,6)
        call setGenGammaCDF(cdf(:,1), point, 1.0, 0.5, 0.5, info)
        call setGenGammaCDF(cdf(:,2), point, 2.0, 0.5, 1.0, info)
        call setGenGammaCDF(cdf(:,3), point, 0.5, 2.0, 0.5, info)
        call setGenGammaCDF(cdf(:,4), point, 0.2, 5.0, 0.2, info)
        call setGenGammaCDF(cdf(:,5), point, .14, 7.0, .14, info)
        call setGenGammaCDF(cdf(:,6), point, 2.0, 5.0, 0.3, info)
        open(newunit = fileUnit, file = "setGenGammaCDF.RK.txt")
        if (any(info < 0)) error stop 'The computation of the cdf info.'
        write(fileUnit,"(7(g0,:,' '))") (point(i), cdf(i,:), i = 1, size(point))
        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 Cumulative Distribution Function (CDF) of GenGamma distribution at the specified values.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the cdf at an input scalar real value.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
call setGenGammaCDF(cdf(1), 0.5_RK, info(1))
if (info(1) < 0) error stop 'The computation of the cdf info.'
cdf(1)
+0.393469363
 
 
kappa(1)
+0.500000000
call setGenGammaCDF(cdf(1), 0.5_RK, kappa(1), info(1))
if (info(1) < 0) error stop 'The computation of the cdf info.'
cdf(1)
+0.682689488
 
 
kappa(1)
+0.500000000
invOmega(1)
+0.999999940E-1
call setGenGammaCDF(cdf(1), 0.5_RK, kappa(1), invOmega(1), info(1))
if (info(1) < 0) error stop 'The computation of the cdf info.'
cdf(1)
+0.828073680
 
 
kappa(1)
+0.500000000
invOmega(1)
+0.999999940E-1
call setGenGammaCDF(cdf(1), 0.5_RK, kappa(1), invOmega(1), invSigma(1), info(1))
if (info(1) < 0) error stop 'The computation of the cdf info.'
cdf(1)
+0.760309935
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the cdf at an input vector real value with different parameter values.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
kappa(1)
+0.500000000
call setGenGammaCDF(cdf(1:NP:NP/5), 0.5_RK, kappa(1:NP:NP/5), info(1:NP:NP/5))
if (info(1) < 0) error stop 'The computation of the cdf info.'
cdf(1:NP:NP/5)
+0.682689488, +0.499022126, +0.346280664, +0.229651660, +0.146336332
 
 
kappa(1)
+0.500000000
call setGenGammaCDF(cdf(1:NP:NP/5), point(1:NP:NP/5), kappa(1:NP:NP/5), info(1:NP:NP/5))
if (any(info(1:NP:NP/5) < 0)) error stop 'The computation of the cdf info.'
cdf(1:NP:NP/5)
+0.112462923, +0.800254866E-1, +0.116214290, +0.297623754, +0.788579822
 
 

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
 
fontsize = 17
 
marker ={ "CK" : "-"
        , "IK" : "."
        , "RK" : "-"
        }
xlab =  { "CK" : "X ( real/imaginary components )"
        , "IK" : "X ( integer-valued )"
        , "RK" : "X ( real-valued )"
        }
legends =   [ "$\kappa, 1/\omega, 1/\sigma = 1.0, 0.5, 0.5$"
            , "$\kappa, 1/\omega, 1/\sigma = 2.0, 0.5, 1.0$"
            , "$\kappa, 1/\omega, 1/\sigma = 0.5, 2.0, 0.5$"
            , "$\kappa, 1/\omega, 1/\sigma = 0.2, 5.0, 0.2$"
            , "$\kappa, 1/\omega, 1/\sigma = .14, 7.0, .14$"
            , "$\kappa, 1/\omega, 1/\sigma = 2.0, 5.0, 0.3$"
            ]
 
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:len(legends)+1]
                    , marker[kind]
                   #, color = "r"
                    )
            plt.plot( df.values[:, 1]
                    , df.values[:,1:len(legends)+1]
                    , marker[kind]
                   #, color = "blue"
                    )
        else:
            plt.plot( df.values[:, 0]
                    , df.values[:,1:len(legends)+1]
                    , marker[kind]
                   #, color = "r"
                    )
            ax.legend   ( legends
                        , fontsize = fontsize
                       #, loc = "center right"
                        )
 
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        ax.set_xlabel(xlab[kind], fontsize = 17)
        ax.set_ylabel("Cumulative Distribution Function (CDF)", fontsize = 17)
        ax.set_xlim([0, 8.])
 
        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.savefig(fileList[0].replace(".txt",".png"))
 
    elif len(fileList) > 1:
 
        sys.exit("Ambiguous file list exists.")

Visualization of the example output ⛓

Test:

test_pm_distGenGamma

Todo:

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

Final Remarks ⛓

---

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
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 1094 of file pm_distGenGamma.F90.

---

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

• src/fortran/main/pm_distGenGamma.F90