ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_distExpGamma::setExpGammaCDF Interface Reference

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

call setExpGammaCDF(cdf, x, info)
call setExpGammaCDF(cdf, x, kappa, info)
call setExpGammaCDF(cdf, x, kappa, logSigma, info)
Return the Cumulative Distribution Function (CDF) of the ExpGamma distribution for an input x within ...
This module contains classes and procedures for computing various statistical quantities related to t...
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
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
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
Generate count evenly-logarithmically-spaced points over the interval [base**logx1,...
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
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
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
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
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
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
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.

  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.

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: