pm_distGenGamma::setGenGammaRand Interface Reference

Return a scalar or array of arbitrary rank of GenGamma-distributed random values with the specified shape and scale parameters \((\kappa, \omega, \sigma)\) of the Generalized Gamma distribution corresponding to the procedure arguments (kappa, omega, sigma). More...

Detailed Description

Return a scalar or array of arbitrary rank of GenGamma-distributed random values with the specified shape and scale parameters \((\kappa, \omega, \sigma)\) of the Generalized Gamma distribution corresponding to the procedure arguments (kappa, omega, sigma).

See the documentation of pm_distGenGamma for more information on the Probability Density Function (PDF) of the Generalized Gamma distribution.

Parameters

[in,out]	rng	: The input/output scalar that can be an object of, type rngf_type, implying the use of intrinsic Fortran uniform RNG for Gamma RNG. type xoshiro256ssw_type, implying the use of xoshiro256** uniform RNG for Gamma RNG. (optional, default = rngf_type, implying the use of the intrinsic Fortran URNG.)
[out]	rand	: The output scalar or array of rank 1, or array of arbitrary rank if the rng argument is missing or set to rngf_type, or of, type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128). On output, it contains GenGamma-distributed random value(s).
[in]	kappa	: The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as rand, representing the \(\kappa\) shape parameter of the Generalized Gamma distribution.
[in]	sigma	: The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as rand, representing the \(\omega\) shape parameter of the Generalized Gamma distribution.
[in]	sigma	: The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as rand, representing the \(\sigma\) scale parameter of the Generalized Gamma distribution.

Possible calling interfaces ⛓

use pm_distGenGamma, only: setGenGammaRand
 
call setGenGammaRand(rand, kappa, omega, sigma)
call setGenGammaRand(rand(..), kappa, omega, sigma)
call setGenGammaRand(rng, rand, kappa, omega, sigma)
call setGenGammaRand(rng, rand(:), kappa, omega, sigma)

Warning

The condition 0 < kappa must hold for the corresponding input arguments.
The condition 0 < omega must hold for the corresponding input arguments.
The condition 0 < sigma must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

Remarks

The procedures under discussion are impure.

The procedures under discussion are elemental.

The procedures under discussion are recursive.

Note

For repeated Gamma RNG with fixed kappa, it is best to pass a vector of rand to be filled with random numbers rather than calling the procedures with scalar rand argument repeatedly.
In addition to avoiding procedure call overhead, vectorized RGN in this particular case also avoids an unnecessary division and square-root operation.

See also

getGenGammaLogPDF
setGenGammaLogPDF
getGenGammaCDF
setGenGammaCDF

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_kind, only: RKG => RKS ! all real kinds are supported.
    use pm_distGenGamma, only: setGenGammaRand
    use pm_arraySpace, only: setLinSpace
    use pm_arraySpace, only: setLogSpace
    use pm_io, only: display_type
 
    implicit none
 
    integer(IK), parameter  :: NP = 10000_IK
    real(RKG), dimension(NP) :: kappa, omega, sigma, rand, mean
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call setLogSpace(kappa, logx1 = log(0.1_RKG), logx2 = log(10._RKG))
    call setLogSpace(sigma, logx1 = log(0.1_RKG), logx2 = log(10._RKG))
    call setLogSpace(omega, logx1 = log(0.1_RKG), logx2 = log(10._RKG))
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Generate random numbers from the GenGamma distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("sigma(1:NP:NP/3)")
    call disp%show( sigma(1:NP:NP/3) )
    call disp%show("call setGenGammaRand(rand(1:NP:NP/3), kappa(1), omega(1), sigma(1:NP:NP/3))")
                    call setGenGammaRand(rand(1:NP:NP/3), kappa(1), omega(1), sigma(1:NP:NP/3))
    call disp%show("rand(1:NP:NP/3)")
    call disp%show( rand(1:NP:NP/3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("kappa(1:NP:NP/3)")
    call disp%show( kappa(1:NP:NP/3) )
    call disp%show("call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1))")
                    call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1))
    call disp%show("rand(1:NP:NP/3)")
    call disp%show( rand(1:NP:NP/3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("kappa(1:NP:NP/3)")
    call disp%show( kappa(1:NP:NP/3) )
    call disp%show("sigma(1:NP:NP/3)")
    call disp%show( sigma(1:NP:NP/3) )
    call disp%show("call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1:NP:NP/3))")
                    call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1:NP:NP/3))
    call disp%show("rand(1:NP:NP/3)")
    call disp%show( rand(1:NP:NP/3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Test the mean of a random sample against the analytic answer.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    block
        use pm_sampleMean, only: getMean
        use pm_distExp, only: getExpRand
        real(RKG) :: kappa, omega, sigma, mean
        integer(IK) :: itry
        do itry = 1, 10
            call disp%skip()
            call disp%show("kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)")
                            kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
            call disp%show("[kappa, omega, sigma]")
            call disp%show( [kappa, omega, sigma] )
            call disp%show("call setGenGammaRand(rand, kappa, omega, sigma)")
                            call setGenGammaRand(rand, kappa, omega, sigma)
            call disp%show("mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma")
                            mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
            call disp%show("[getMean(rand), mean]")
            call disp%show( [getMean(rand), mean] )
            call disp%skip()
        end do
    end block
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example rand array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_io, only: getErrTableWrite
        integer(IK) :: fileUnit, i
        integer(IK), parameter :: NP = 5000
        real(RKG), dimension(NP, 5) :: rand
        call setGenGammaRand(rand(:,1), 2.0_RKG, omega = 1 / 5.0_RKG, sigma = 1 / 0.3_RKG)
        call setGenGammaRand(rand(:,2), .14_RKG, omega = 1 / 7.0_RKG, sigma = 1 / .14_RKG)
        call setGenGammaRand(rand(:,3), 0.2_RKG, omega = 1 / 5.0_RKG, sigma = 1 / 0.2_RKG)
        call setGenGammaRand(rand(:,4), 0.5_RKG, omega = 1 / 2.0_RKG, sigma = 1 / 0.5_RKG)
        call setGenGammaRand(rand(:,5), 2.0_RKG, omega = 1 / 0.5_RKG, sigma = 1 / 1.0_RKG)
        !call setGenGammaRand(rand(:,6), 1.0_RKG, omega = 1 / 0.5_RKG, sigma = 1 / 0.5_RKG)
        if (0 /= getErrTableWrite("setGenGammaRand.RKG.txt", rand)) error stop 'table write failed.'
    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 ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Generate random numbers from the GenGamma distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
sigma(1:NP:NP/3)
+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010
call setGenGammaRand(rand(1:NP:NP/3), kappa(1), omega(1), sigma(1:NP:NP/3))
rand(1:NP:NP/3)
+0.246609062, +0.139011100, +0.136816716E-1, +1.10822439
 
 
kappa(1:NP:NP/3)
+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010
call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1))
rand(1:NP:NP/3)
+0.262083739, +0.769532561, +0.854447424, +1.02380049
 
 
kappa(1:NP:NP/3)
+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010
sigma(1:NP:NP/3)
+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010
call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1:NP:NP/3))
rand(1:NP:NP/3)
+0.719341516, +0.817872584, +1.19199896, +1.61687899
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Test the mean of a random sample against the analytic answer.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+2.10582089, +1.42327619, +1.43380165
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+5.38940287, +4.68922806
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+0.285340518, +1.10786247, +0.442904979E-1
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+0.901213195E-2, +0.124671636E-1
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+1.52903306, +2.27296162, +2.85300994
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+56.5402489, +15.1260548
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+2.89707136, +0.707545221, +0.948019326
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+1.96237516, +1.94352341
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+0.134042829, +1.34755206, +0.744359493
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+0.821327195E-1, +0.941710770E-1
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+0.308452100, +0.946370885E-1, +0.120554298
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+0.620471478, +0.913114101E-1
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+0.885772765, +0.776675165, +0.170950890
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+0.213991478, +0.142734900
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+0.838939939E-2, +4.51184702, +0.416142523
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+0.544949714E-2, +0.419685133E-1
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+2.75959492, +0.126669332, +0.102064475
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+0.834350884, +0.113669977
 
 
kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)
[kappa, omega, sigma]
+0.196212322, +0.950398564, +0.410032123
call setGenGammaRand(rand, kappa, omega, sigma)
mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma
[getMean(rand), mean]
+0.863392651E-1, +0.817650780E-1
 
 

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 ={ "CKG" : "-"
        , "IKG" : "."
        , "RKG" : "-"
        }
xlab =  { "CKG" : "Generalized Gamma Random Value ( real/imaginary components )"
        , "IKG" : "Generalized Gamma Random Value ( integer-valued )"
        , "RKG" : "Generalized Gamma Random Value ( 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 ["IKG", "CKG", "RKG"]:
 
    pattern = "*." + kind + ".txt"
    fileList = glob.glob(pattern)
    if len(fileList) == 1:
 
        df = pd.read_csv(fileList[0], delimiter = ",", header = None)
 
        fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
        ax = plt.subplot()
 
        for j in range(len(df.values[0,:])):
            if kind == "CKG":
                plt.hist( df.values[:,j]
                        , histtype = "stepfilled"
                        , alpha = 0.5
                        , bins = 75
                        )
            else:
                plt.hist( df.values[:,j]
                        , histtype = "stepfilled"
                        , alpha = 0.5
                        , bins = 75
                        )
                ax.legend   ( legends
                            , fontsize = fontsize
                            )
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        ax.set_xlabel(xlab[kind], fontsize = 17)
        ax.set_ylabel("Count", fontsize = 17)
        ax.set_title("Histograms of {} Generalized Gamma random values".format(len(df.values[:, 0])), fontsize = 17)
        #ax.set_yscale("log")
 
        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

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 1435 of file pm_distGenGamma.F90.

---

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

• src/fortran/main/pm_distGenGamma.F90