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)

pm_distGenGamma::setGenGammaRand
Return a scalar or array of arbitrary rank of GenGamma-distributed random values with the specified s...
Definition: pm_distGenGamma.F90:1435

pm_distGenGamma
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distGenGamma.F90:129

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 ⛓

: 1program example

2

3 use pm_kind, only: SK, IK

4 use pm_kind, only: RKG => RKS ! all real kinds are supported.

5 use pm_distGenGamma, only: setGenGammaRand

6 use pm_arraySpace, only: setLinSpace

7 use pm_arraySpace, only: setLogSpace

8 use pm_io, only: display_type

9

10 implicit none

11

12 integer(IK), parameter :: NP = 10000_IK

13 real(RKG), dimension(NP) :: kappa, omega, sigma, rand, mean

14

15 type(display_type) :: disp

16 disp = display_type(file = "main.out.F90")

17

18 call setLogSpace(kappa, logx1 = log(0.1_RKG), logx2 = log(10._RKG))

19 call setLogSpace(sigma, logx1 = log(0.1_RKG), logx2 = log(10._RKG))

20 call setLogSpace(omega, logx1 = log(0.1_RKG), logx2 = log(10._RKG))

21

22 call disp%skip()

23 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

24 call disp%show("! Generate random numbers from the GenGamma distribution.")

25 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

26 call disp%skip()

27

28 call disp%skip()

29 call disp%show("sigma(1:NP:NP/3)")

30 call disp%show( sigma(1:NP:NP/3) )

31 call disp%show("call setGenGammaRand(rand(1:NP:NP/3), kappa(1), omega(1), sigma(1:NP:NP/3))")

32 call setGenGammaRand(rand(1:NP:NP/3), kappa(1), omega(1), sigma(1:NP:NP/3))

33 call disp%show("rand(1:NP:NP/3)")

34 call disp%show( rand(1:NP:NP/3) )

35 call disp%skip()

36

37 call disp%skip()

38 call disp%show("kappa(1:NP:NP/3)")

39 call disp%show( kappa(1:NP:NP/3) )

40 call disp%show("call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1))")

41 call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1))

42 call disp%show("rand(1:NP:NP/3)")

43 call disp%show( rand(1:NP:NP/3) )

44 call disp%skip()

45

46 call disp%skip()

47 call disp%show("kappa(1:NP:NP/3)")

48 call disp%show( kappa(1:NP:NP/3) )

49 call disp%show("sigma(1:NP:NP/3)")

50 call disp%show( sigma(1:NP:NP/3) )

51 call disp%show("call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1:NP:NP/3))")

52 call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1:NP:NP/3))

53 call disp%show("rand(1:NP:NP/3)")

54 call disp%show( rand(1:NP:NP/3) )

55 call disp%skip()

56

57 call disp%skip()

58 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

59 call disp%show("! Test the mean of a random sample against the analytic answer.")

60 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

61 call disp%skip()

62

63 block

64 use pm_sampleMean, only: getMean

65 use pm_distExp, only: getExpRand

66 real(RKG) :: kappa, omega, sigma, mean

67 integer(IK) :: itry

68 do itry = 1, 10

69 call disp%skip()

70 call disp%show("kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)")

71 kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

72 call disp%show("[kappa, omega, sigma]")

73 call disp%show( [kappa, omega, sigma] )

74 call disp%show("call setGenGammaRand(rand, kappa, omega, sigma)")

75 call setGenGammaRand(rand, kappa, omega, sigma)

76 call disp%show("mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma")

77 mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

78 call disp%show("[getMean(rand), mean]")

79 call disp%show( [getMean(rand), mean] )

80 call disp%skip()

81 end do

82 end block

83

84 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

85 ! Output an example rand array for visualization.

86 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

87

88 block

89 use pm_io, only: getErrTableWrite

90 integer(IK) :: fileUnit, i

91 integer(IK), parameter :: NP = 5000

92 real(RKG), dimension(NP, 5) :: rand

93 call setGenGammaRand(rand(:,1), 2.0_RKG, omega = 1 / 5.0_RKG, sigma = 1 / 0.3_RKG)

94 call setGenGammaRand(rand(:,2), .14_RKG, omega = 1 / 7.0_RKG, sigma = 1 / .14_RKG)

95 call setGenGammaRand(rand(:,3), 0.2_RKG, omega = 1 / 5.0_RKG, sigma = 1 / 0.2_RKG)

96 call setGenGammaRand(rand(:,4), 0.5_RKG, omega = 1 / 2.0_RKG, sigma = 1 / 0.5_RKG)

97 call setGenGammaRand(rand(:,5), 2.0_RKG, omega = 1 / 0.5_RKG, sigma = 1 / 1.0_RKG)

98 !call setGenGammaRand(rand(:,6), 1.0_RKG, omega = 1 / 0.5_RKG, sigma = 1 / 0.5_RKG)

99 if (0 /= getErrTableWrite("setGenGammaRand.RKG.txt", rand)) error stop 'table write failed.'

100 end block

101

102end program example

pm_arraySpace::setLinSpace
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
Definition: pm_arraySpace.F90:324

pm_arraySpace::setLogSpace
Return the logSpace output argument with size(logSpace) elements of logarithmically-evenly-spaced val...
Definition: pm_arraySpace.F90:765

pm_distExp::getExpRand
Return a scalar (or array of arbitrary rank of) random value(s) from the Exponential distribution,...
Definition: pm_distExp.F90:1022

pm_io::getErrTableWrite
Generate and return the iostat code resulting from writing the input table of rank 1 or 2 to the spec...
Definition: pm_io.F90:5940

pm_io::show
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508

pm_sampleMean::getMean
Generate and return the (weighted) mean of an input sample of nsam observations with ndim = 1 or 2 at...
Definition: pm_sampleMean.F90:229

pm_arraySpace
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
Definition: pm_arraySpace.F90:33

pm_distExp
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distExp.F90:112

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567

pm_sampleMean
This module contains classes and procedures for computing the first moment (i.e., the statistical mea...
Definition: pm_sampleMean.F90:104

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1

2!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

3! Generate random numbers from the GenGamma distribution.

4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

5

6

7sigma(1:NP:NP/3)

8+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010

9call setGenGammaRand(rand(1:NP:NP/3), kappa(1), omega(1), sigma(1:NP:NP/3))

10rand(1:NP:NP/3)

11+0.201517209, +0.635577023, +1.05917287, +0.255406827

12

13

14kappa(1:NP:NP/3)

15+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010

16call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1))

17rand(1:NP:NP/3)

18+0.128199920, +0.537410200, +0.921142042, +0.948806047

19

20

21kappa(1:NP:NP/3)

22+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010

23sigma(1:NP:NP/3)

24+0.999999940E-1, +0.464158833, +2.15443444, +10.0000010

25call setGenGammaRand(rand(1:NP:NP/3), kappa(1:NP:NP/3), omega(1), sigma(1:NP:NP/3))

26rand(1:NP:NP/3)

27+0.304028064, +0.983291864, +1.20070076, +1.63292384

28

29

30!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

31! Test the mean of a random sample against the analytic answer.

32!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

33

34

35kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

36[kappa, omega, sigma]

37+0.118433610, +1.76840603, +0.238065094

38call setGenGammaRand(rand, kappa, omega, sigma)

39mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

40[getMean(rand), mean]

41+0.940355472E-2, +0.285875555E-1

42

43

44kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

45[kappa, omega, sigma]

46+0.735983193, +0.488733977, +2.65539241

47call setGenGammaRand(rand, kappa, omega, sigma)

48mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

49[getMean(rand), mean]

50+1.17687404, +1.94586015

51

52

53kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

54[kappa, omega, sigma]

55+0.817604482, +0.926701427, +0.226678830E-1

56call setGenGammaRand(rand, kappa, omega, sigma)

57mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

58[getMean(rand), mean]

59+0.240387097E-1, +0.181691963E-1

60

61

62kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

63[kappa, omega, sigma]

64+0.251981586, +0.439205617, +0.354121953

65call setGenGammaRand(rand, kappa, omega, sigma)

66mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

67[getMean(rand), mean]

68+0.229920506, +0.129242703

69

70

71kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

72[kappa, omega, sigma]

73+0.938574135, +1.88003635, +0.232350230

74call setGenGammaRand(rand, kappa, omega, sigma)

75mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

76[getMean(rand), mean]

77+0.111541227, +0.380699128

78

79

80kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

81[kappa, omega, sigma]

82+0.235162284E-1, +0.408348411, +0.924319252E-1

83call setGenGammaRand(rand, kappa, omega, sigma)

84mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

85[getMean(rand), mean]

86+0.181683563E-1, +0.451823464E-2

87

88

89kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

90[kappa, omega, sigma]

91+0.651876302E-2, +1.55385983, +1.87328064

92call setGenGammaRand(rand, kappa, omega, sigma)

93mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

94[getMean(rand), mean]

95+0.116354022E-1, +0.109047573E-1

96

97

98kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

99[kappa, omega, sigma]

100+0.665255249, +0.212612793, +0.936376929

101call setGenGammaRand(rand, kappa, omega, sigma)

102mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

103[getMean(rand), mean]

104+0.782816112, +0.750369072

105

106

107kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

108[kappa, omega, sigma]

109+0.201095149, +3.31672597, +0.539041996

110call setGenGammaRand(rand, kappa, omega, sigma)

111mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

112[getMean(rand), mean]

113+0.100796334, +0.400290966

114

115

116kappa = getExpRand(1._RKG); omega = getExpRand(1._RKG); sigma = getExpRand(1._RKG)

117[kappa, omega, sigma]

118+0.313700065E-1, +3.79540992, +0.905819356

119call setGenGammaRand(rand, kappa, omega, sigma)

120mean = exp(log_gamma(kappa + omega) - log_gamma(kappa)) * sigma

121[getMean(rand), mean]

122+0.718467236E-1, +0.140155211

123

124

Postprocessing of the example output ⛓
1#!/usr/bin/env python

2

3import matplotlib.pyplot as plt

4import pandas as pd

5import numpy as np

6import glob

7import sys

8

9linewidth = 2

10fontsize = 17

11

12marker ={ "CKG" : "-"

13 , "IKG" : "."

14 , "RKG" : "-"

15 }

16xlab = { "CKG" : "Generalized Gamma Random Value ( real/imaginary components )"

17 , "IKG" : "Generalized Gamma Random Value ( integer-valued )"

18 , "RKG" : "Generalized Gamma Random Value ( real-valued )"

19 }

20legends = [ "$\kappa, 1/\omega, 1/\sigma = 1.0, 0.5, 0.5$"

21 , "$\kappa, 1/\omega, 1/\sigma = 2.0, 0.5, 1.0$"

22 , "$\kappa, 1/\omega, 1/\sigma = 0.5, 2.0, 0.5$"

23 , "$\kappa, 1/\omega, 1/\sigma = 0.2, 5.0, 0.2$"

24 , "$\kappa, 1/\omega, 1/\sigma = .14, 7.0, .14$"

25 , "$\kappa, 1/\omega, 1/\sigma = 2.0, 5.0, 0.3$"

26 ]

27

28for kind in ["IKG", "CKG", "RKG"]:

29

30 pattern = "*." + kind + ".txt"

31 fileList = glob.glob(pattern)

32 if len(fileList) == 1:

33

34 df = pd.read_csv(fileList[0], delimiter = ",", header = None)

35

36 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)

37 ax = plt.subplot()

38

39 for j in range(len(df.values[0,:])):

40 if kind == "CKG":

41 plt.hist( df.values[:,j]

42 , histtype = "stepfilled"

43 , alpha = 0.5

44 , bins = 75

45 )

46 else:

47 plt.hist( df.values[:,j]

48 , histtype = "stepfilled"

49 , alpha = 0.5

50 , bins = 75

51 )

52 ax.legend ( legends

53 , fontsize = fontsize

54 )

55 plt.xticks(fontsize = fontsize - 2)

56 plt.yticks(fontsize = fontsize - 2)

57 ax.set_xlabel(xlab[kind], fontsize = 17)

58 ax.set_ylabel("Count", fontsize = 17)

59 ax.set_title("Histograms of {} Generalized Gamma random values".format(len(df.values[:, 0])), fontsize = 17)

60 #ax.set_yscale("log")

61

62 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")

63 ax.tick_params(axis = "y", which = "minor")

64 ax.tick_params(axis = "x", which = "minor")

65

66 plt.savefig(fileList[0].replace(".txt",".png"))

67

68 elif len(fileList) > 1:

69

70 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.

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.
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