Return the Cumulative Distribution Function (CDF) of the GenExpGamma distribution for an input x
within the support of the distribution \(x \in (-\infty,+\infty)\).
More...
Return the Cumulative Distribution Function (CDF) of the GenExpGamma distribution for an input x
within the support of the distribution \(x \in (-\infty,+\infty)\).
See the documentation of pm_distGenExpGamma for more information on the GenExpGamma 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-like arguments, of the same type and kind as x , containing the inverse scale 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 ⛓
Return the Cumulative Distribution Function (CDF) of the GenExpGamma distribution for an input x with...
This module contains classes and procedures for computing various statistical quantities related to t...
- Warning
- The condition
kappa > 0
and invOmega > 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.
- See also
- getGenExpGammaCDF
Example usage ⛓
13 integer(IK) ,
parameter :: NP
= 1000_IK
14 real(RK) , dimension(NP) :: point, CDF, kappa, invOmega, logSigma
15 integer(IK) :: info(NP)
17 type(display_type) :: disp
21 invOmega
= getLogSpace(logx1
= log(
0.1_RK), logx2
= log(
10._RK), count
= NP)
26 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
27 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
28 call disp%show(
"! Compute the Cumulative Distribution Function (CDF) of GenExpGamma distribution at the specified values.")
29 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
30 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
34 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
35 call disp%show(
"! Compute the CDF at an input scalar real value.")
36 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
40 call disp%show(
"call setGenExpGammaCDF(CDF(1), 0.5_RK, info(1))")
42 call disp%show(
"if (info(1) < 0) error stop 'The computation of the CDF info.'")
43 if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
51 call disp%show(
"call setGenExpGammaCDF(CDF(1), 0.5_RK, kappa(1), info(1))")
53 call disp%show(
"if (info(1) < 0) error stop 'The computation of the CDF info.'")
54 if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
64 call disp%show(
"call setGenExpGammaCDF(CDF(1), 0.5_RK, kappa(1), invOmega(1), info(1))")
66 call disp%show(
"if (info(1) < 0) error stop 'The computation of the CDF info.'")
67 if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
77 call disp%show(
"call setGenExpGammaCDF(CDF(1), 0.5_RK, kappa(1), invOmega(1), logSigma(1), info(1))")
78 call setGenExpGammaCDF(CDF(
1),
0.5_RK, kappa(
1), invOmega(
1), logSigma(
1), info(
1))
79 call disp%show(
"if (info(1) < 0) error stop 'The computation of the CDF info.'")
80 if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
86 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
87 call disp%show(
"! Compute the CDF at an input vector real value with different parameter values.")
88 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
94 call disp%show(
"call setGenExpGammaCDF(CDF(1:NP:NP/5), 0.5_RK, kappa(1:NP:NP/5), info(1:NP:NP/5))")
96 call disp%show(
"if (info(1) < 0) error stop 'The computation of the CDF info.'")
97 if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
105 call disp%show(
"call setGenExpGammaCDF(CDF(1:NP:NP/5), point(1:NP:NP/5), kappa(1:NP:NP/5), info(1:NP:NP/5))")
106 call setGenExpGammaCDF(CDF(
1:NP:NP
/5), point(
1:NP:NP
/5), kappa(
1:NP:NP
/5), info(
1:NP:NP
/5))
107 call disp%show(
"if (any(info(1:NP:NP/5) < 0)) error stop 'The computation of the CDF info.'")
108 if (
any(info(
1:NP:NP
/5)
< 0))
error stop 'The computation of the CDF info.'
118 integer :: fileUnit, i
119 real(RK) :: CDF(NP,
6)
126 open(newunit
= fileUnit, file
= "setGenExpGammaCDF.RK.txt")
127 if (
any(info
< 0))
error stop 'The computation of the CDF info.'
128 write(fileUnit,
"(7(g0,:,' '))") (point(i), CDF(i,:), i
= 1,
size(point))
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.
This is a generic method of the derived type display_type with pass attribute.
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...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in C-Fortran Interoperati...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example Windows Batch compile command via Intel ifort
compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
15if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
23if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
33if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
42call setGenExpGammaCDF(CDF(
1),
0.5_RK, kappa(
1), invOmega(
1), logSigma(
1), info(
1))
43if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
56if (info(
1)
< 0)
error stop 'The computation of the CDF info.'
58+0.930612206,
+0.862185597,
+0.778141320,
+0.684153199,
+0.586314142
63call setGenExpGammaCDF(CDF(
1:NP:NP
/5), point(
1:NP:NP
/5), kappa(
1:NP:NP
/5), info(
1:NP:NP
/5))
64if (
any(info(
1:NP:NP
/5)
< 0))
error stop 'The computation of the CDF info.'
66+0.760284485E-2,
+0.883790851E-2,
+0.993758515E-1,
+0.998501480,
+1.00000000
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
15xlab = {
"CK" :
"X ( real/imaginary components )"
16 ,
"IK" :
"X ( integer-valued )"
17 ,
"RK" :
"X ( real-valued )"
19legends = [
"$\kappa = 0.5, \omega = 0.5$"
20 ,
"$\kappa = 1.0, \omega = 0.5$"
21 ,
"$\kappa = 2.0, \omega = 0.5$"
22 ,
"$\kappa = 0.5, \omega = 2.0$"
23 ,
"$\kappa = 1.0, \omega = 2.0$"
24 ,
"$\kappa = 2.0, \omega = 2.0$"
27for kind
in [
"IK",
"CK",
"RK"]:
29 pattern =
"*." + kind +
".txt"
30 fileList = glob.glob(pattern)
31 if len(fileList) == 1:
33 df = pd.read_csv(fileList[0], delimiter =
" ")
35 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
39 plt.plot( df.values[:, 0]
40 , df.values[:,1:len(legends)+1]
44 plt.plot( df.values[:, 1]
45 , df.values[:,1:len(legends)+1]
50 plt.plot( df.values[:, 0]
51 , df.values[:,1:len(legends)+1]
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)
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")
68 plt.savefig(fileList[0].replace(
".txt",
".png"))
70 elif len(fileList) > 1:
72 sys.exit(
"Ambiguous file list exists.")
Visualization of the example output ⛓
- Test:
- test_pm_distGenExpGamma
- 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 1072 of file pm_distGenExpGamma.F90.