Return the Cumulative Distribution Function (CDF) of the ExpGamma distribution for an input x within the support of the distribution $x \in (-\infty,+\infty)$. More...

Detailed Description

Return the Cumulative Distribution Function (CDF) of the ExpGamma distribution for an input x within the support of the distribution $x \in (-\infty,+\infty)$.

See the documentation of pm_distExpGamma for more information on the ExpGamma 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 `logSigma` is also present.)
[in]	logSigma	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as `x`, containing the location 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_distExpGamma, only: setExpGammaCDF

call setExpGammaCDF(cdf, x, info)

call setExpGammaCDF(cdf, x, kappa, info)

call setExpGammaCDF(cdf, x, kappa, logSigma, info)

pm_distExpGamma::setExpGammaCDF
Return the Cumulative Distribution Function (CDF) of the ExpGamma distribution for an input x within ...
Definition: pm_distExpGamma.F90:855

pm_distExpGamma
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distExpGamma.F90:91

Warning: 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: getExpGammaCDF

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK

4 use pm_kind, only: IK, LK

5 use pm_kind, only: RK => RKS ! all other real kinds are also supported.

6 use pm_io, only: display_type

7 use pm_arraySpace, only: getLinSpace

8 use pm_arraySpace, only: getLogSpace

9 use pm_distExpGamma, only: setExpGammaCDF

10

11 implicit none

12

13 integer(IK) , parameter :: NP = 1000_IK

14 real(RK) , dimension(NP) :: point, CDF, kappa, logSigma

15 integer(IK) :: info(NP)

16

17 type(display_type) :: disp

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

19

20 kappa = getLinSpace(+0.5_RK, +2._RK, count = NP)

21 logSigma = getLinSpace(-3._RK, +3._RK, count = NP)

22 point = getLinSpace(-10._RK, +10._RK, count = NP)

23

24 call disp%skip()

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

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

27 call disp%show("! Compute the Cumulative Distribution Function (CDF) of ExpGamma distribution at the specified values.")

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

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

30 call disp%skip()

31

32 call disp%skip()

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

34 call disp%show("! Compute the CDF at an input scalar real value.")

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

36 call disp%skip()

37

38 call disp%skip()

39 call disp%show("call setExpGammaCDF(CDF(1), 0.5_RK, info(1))")

40 call setExpGammaCDF(CDF(1), 0.5_RK, info(1))

41 call disp%show("if (info(1) < 0) error stop 'The computation of the CDF info.'")

42 if (info(1) < 0) error stop 'The computation of the CDF info.'

43 call disp%show("CDF(1)")

44 call disp%show( CDF(1) )

45 call disp%skip()

46

47 call disp%skip()

48 call disp%show("kappa(1)")

49 call disp%show( kappa(1) )

50 call disp%show("call setExpGammaCDF(CDF(1), 0.5_RK, kappa(1), info(1))")

51 call setExpGammaCDF(CDF(1), 0.5_RK, kappa(1), info(1))

52 call disp%show("if (info(1) < 0) error stop 'The computation of the CDF info.'")

53 if (info(1) < 0) error stop 'The computation of the CDF info.'

54 call disp%show("CDF(1)")

55 call disp%show( CDF(1) )

56 call disp%skip()

57

58 call disp%skip()

59 call disp%show("kappa(1)")

60 call disp%show( kappa(1) )

61 call disp%show("call setExpGammaCDF(CDF(1), 0.5_RK, kappa(1), info(1))")

62 call setExpGammaCDF(CDF(1), 0.5_RK, kappa(1), info(1))

63 call disp%show("if (info(1) < 0) error stop 'The computation of the CDF info.'")

64 if (info(1) < 0) error stop 'The computation of the CDF info.'

65 call disp%show("CDF(1)")

66 call disp%show( CDF(1) )

67 call disp%skip()

68

69 call disp%skip()

70 call disp%show("kappa(1)")

71 call disp%show( kappa(1) )

72 call disp%show("call setExpGammaCDF(CDF(1), 0.5_RK, kappa(1), logSigma(1), info(1))")

73 call setExpGammaCDF(CDF(1), 0.5_RK, kappa(1), logSigma(1), info(1))

74 call disp%show("if (info(1) < 0) error stop 'The computation of the CDF info.'")

75 if (info(1) < 0) error stop 'The computation of the CDF info.'

76 call disp%show("CDF(1)")

77 call disp%show( CDF(1) )

78 call disp%skip()

79

80 call disp%skip()

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

82 call disp%show("! Compute the CDF at an input vector real value with different parameter values.")

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

84 call disp%skip()

85

86 call disp%skip()

87 call disp%show("kappa(1)")

88 call disp%show( kappa(1) )

89 call disp%show("call setExpGammaCDF(CDF(1:NP:NP/5), 0.5_RK, kappa(1:NP:NP/5), info(1:NP:NP/5))")

90 call setExpGammaCDF(CDF(1:NP:NP/5), 0.5_RK, kappa(1:NP:NP/5), info(1:NP:NP/5))

91 call disp%show("if (info(1) < 0) error stop 'The computation of the CDF info.'")

92 if (info(1) < 0) error stop 'The computation of the CDF info.'

93 call disp%show("CDF(1:NP:NP/5)")

94 call disp%show( CDF(1:NP:NP/5) )

95 call disp%skip()

96

97 call disp%skip()

98 call disp%show("kappa(1)")

99 call disp%show( kappa(1) )

100 call disp%show("call setExpGammaCDF(CDF(1:NP:NP/5), point(1:NP:NP/5), kappa(1:NP:NP/5), info(1:NP:NP/5))")

101 call setExpGammaCDF(CDF(1:NP:NP/5), point(1:NP:NP/5), kappa(1:NP:NP/5), info(1:NP:NP/5))

102 call disp%show("if (any(info(1:NP:NP/5) < 0)) error stop 'The computation of the CDF info.'")

103 if (any(info(1:NP:NP/5) < 0)) error stop 'The computation of the CDF info.'

104 call disp%show("CDF(1:NP:NP/5)")

105 call disp%show( CDF(1:NP:NP/5) )

106 call disp%skip()

107

108 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

109 ! Output an example array for visualization.

110 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

111

112 block

113 real(RK) :: CDF(NP,6)

114 integer :: fileUnit, i

115 call setExpGammaCDF(CDF(:,1), point, .5_RK, 0.5, info)

116 call setExpGammaCDF(CDF(:,2), point, 1._RK, 0.5, info)

117 call setExpGammaCDF(CDF(:,3), point, 2._RK, 0.5, info)

118 call setExpGammaCDF(CDF(:,4), point, .5_RK, 2.0, info)

119 call setExpGammaCDF(CDF(:,5), point, 1._RK, 2.0, info)

120 call setExpGammaCDF(CDF(:,6), point, 2._RK, 2.0, info)

121 open(newunit = fileUnit, file = "setExpGammaCDF.RK.txt")

122 if (any(info < 0)) error stop 'The computation of the CDF info.'

123 write(fileUnit,"(7(g0,:,' '))") (point(i), CDF(i,:), i = 1, size(point))

124 close(fileUnit)

125 end block

126

127end program example

pm_arraySpace::getLinSpace
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
Definition: pm_arraySpace.F90:108

pm_arraySpace::getLogSpace
Generate count evenly-logarithmically-spaced points over the interval [base**logx1,...
Definition: pm_arraySpace.F90:538

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

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::RK
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in C-Fortran Interoperati...
Definition: pm_kind.F90:543

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541

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_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!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

4! Compute the Cumulative Distribution Function (CDF) of ExpGamma distribution at the specified values.

5!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

6!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

7

8

9!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

10! Compute the CDF at an input scalar real value.

11!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

12

13

14call setExpGammaCDF(CDF(1), 0.5_RK, info(1))

15if (info(1) < 0) error stop 'The computation of the CDF info.'

16CDF(1)

17+0.807704329

18

19

20kappa(1)

21+0.500000000

22call setExpGammaCDF(CDF(1), 0.5_RK, kappa(1), info(1))

23if (info(1) < 0) error stop 'The computation of the CDF info.'

24CDF(1)

25+0.930612206

26

27

28kappa(1)

29+0.500000000

30call setExpGammaCDF(CDF(1), 0.5_RK, kappa(1), info(1))

31if (info(1) < 0) error stop 'The computation of the CDF info.'

32CDF(1)

33+0.930612206

34

35

36kappa(1)

37+0.500000000

38call setExpGammaCDF(CDF(1), 0.5_RK, kappa(1), logSigma(1), info(1))

39if (info(1) < 0) error stop 'The computation of the CDF info.'

40CDF(1)

41+1.00000000

42

43

44!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

45! Compute the CDF at an input vector real value with different parameter values.

46!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

47

48

49kappa(1)

50+0.500000000

51call setExpGammaCDF(CDF(1:NP:NP/5), 0.5_RK, kappa(1:NP:NP/5), info(1:NP:NP/5))

52if (info(1) < 0) error stop 'The computation of the CDF info.'

53CDF(1:NP:NP/5)

54+0.930612206, +0.862185597, +0.778141320, +0.684153199, +0.586314142

55

56

57kappa(1)

58+0.500000000

59call setExpGammaCDF(CDF(1:NP:NP/5), point(1:NP:NP/5), kappa(1:NP:NP/5), info(1:NP:NP/5))

60if (any(info(1:NP:NP/5) < 0)) error stop 'The computation of the CDF info.'

61CDF(1:NP:NP/5)

62+0.760284485E-2, +0.883790851E-2, +0.993758515E-1, +0.998501480, +1.00000000

63

64

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

9fontsize = 17

10

11marker ={ "CK" : "-"

12 , "IK" : "."

13 , "RK" : "-"

14 }

15xlab = { "CK" : "X ( real/imaginary components )"

16 , "IK" : "X ( integer-valued )"

17 , "RK" : "X ( real-valued )"

18 }

19legends = [ "$\kappa = 0.5, \log(\sigma) = 0.5$"

20 , "$\kappa = 1.0, \log(\sigma) = 0.5$"

21 , "$\kappa = 2.0, \log(\sigma) = 0.5$"

22 , "$\kappa = 0.5, \log(\sigma) = 2.0$"

23 , "$\kappa = 1.0, \log(\sigma) = 2.0$"

24 , "$\kappa = 2.0, \log(\sigma) = 2.0$"

25 ]

26

27for kind in ["IK", "CK", "RK"]:

28

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

30 fileList = glob.glob(pattern)

31 if len(fileList) == 1:

32

33 df = pd.read_csv(fileList[0], delimiter = " ")

34

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

36 ax = plt.subplot()

37

38 if kind == "CK":

39 plt.plot( df.values[:, 0]

40 , df.values[:,1:len(legends)+1]

41 , marker[kind]

42 #, color = "r"

43 )

44 plt.plot( df.values[:,1]

45 , df.values[:,1:len(legends)+1]

46 , marker[kind]

47 #, color = "blue"

48 )

49 else:

50 plt.plot( df.values[:, 0]

51 , df.values[:,1:len(legends)+1]

52 , marker[kind]

53 #, color = "r"

54 )

55 ax.legend ( legends

56 , fontsize = fontsize

57 )

58

59 plt.xticks(fontsize = fontsize - 2)

60 plt.yticks(fontsize = fontsize - 2)

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

62 ax.set_ylabel("Cumulative Distribution Function (CDF)", fontsize = 17)

63

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

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

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

67

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

69

70 elif len(fileList) > 1:

71

72 sys.exit("Ambiguous file list exists.")

Visualization of the example output ⛓

Test:: test_pm_distExpGamma

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.

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 855 of file pm_distExpGamma.F90.

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

src/fortran/main/pm_distExpGamma.F90