Generate and return the Cumulative Distribution Function (CDF) of the Generalized Gamma distribution for an input x
within the support of the distribution \(x \in (0,+\infty)\).
More...
Generate and return the Cumulative Distribution Function (CDF) of the Generalized Gamma distribution for an input x
within the support of the distribution \(x \in (0,+\infty)\).
See the documentation of pm_distGenGamma for more information on the GenGamma CDF.
 Parameters

[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 arraylike arguments, of the same type and kind as x , containing the shape parameter of the distribution.
(optional, default = 1. ) 
[in]  invOmega  : The input scalar or array of the same shape as other arrayvalued arguments, containing the inverse of the second shape parameter ( \(\omega\)) of the distribution.
(optional, default = 1. ) 
[in]  invSigma  : The input scalar or array of the same shape as other arraylike arguments, of the same type and kind as x , containing the rate (inverse scale) parameter of the distribution.
(optional, default = 1. ) 
 Returns
cdf
: The output scalar or array of the same shape as any input arraylike argument, of the same type and kind the input argument x
, containing the CDF of the distribution at the specified x
.
Possible calling interfaces ⛓
cdf
= getGenGammaCDF(x, kappa
= kappa, invOmega
= invOmega, invSigma
= invSigma)
Generate and return the Cumulative Distribution Function (CDF) of the Generalized Gamma distribution ...
This module contains classes and procedures for computing various statistical quantities related to t...
 Warning
 The condition \(x \in (0,+\infty)\),
kappa > 0
, invOmega > 0
, and invSigma > 0
must hold for the input values (x, kappa, invOmega, invSigma)
.
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
 setGenGammaCDF
Example usage ⛓
13 integer(IK) ,
parameter :: NP
= 1000_IK
14 real(RK) ,
allocatable :: point(:), cdf(:), kappa(:), invOmega(:), invSigma(:)
16 type(display_type) :: disp
20 invOmega
= getLogSpace(logx1
= log(
0.1_RK), logx2
= log(
10._RK), count
= NP)
22 point
= getLogSpace(
log(.
01_RK),
log(
+10._RK), count
= NP)
23 allocate(cdf,
mold = point)
26 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
27 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
28 call disp%show(
"! Compute the Cumulative Distribution Function (CDF) of GenGamma 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(
"cdf(1) = getGenGammaCDF(0.5_RK)")
49 call disp%show(
"cdf(1) = getGenGammaCDF(0.5_RK, kappa(1))")
60 call disp%show(
"cdf(1) = getGenGammaCDF(0.5_RK, kappa(1), invOmega(1))")
71 call disp%show(
"cdf(1) = getGenGammaCDF(0.5_RK, kappa(1), invOmega(1), invSigma(1))")
72 cdf(
1)
= getGenGammaCDF(
0.5_RK, kappa(
1), invOmega(
1), invSigma(
1))
78 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
79 call disp%show(
"! Compute the cdf at an input vector real value with different parameter values.")
80 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
86 call disp%show(
"cdf(1:NP:NP/5) = getGenGammaCDF(0.5_RK, kappa(1:NP:NP/5))")
95 call disp%show(
"cdf(1:NP:NP/5) = getGenGammaCDF(point(1:NP:NP/5), kappa(1:NP:NP/5))")
96 cdf(
1:NP:NP
/5)
= getGenGammaCDF(point(
1:NP:NP
/5), kappa(
1:NP:NP
/5))
106 integer :: fileUnit, i
107 real(RK) :: cdf(NP,
6)
114 open(newunit
= fileUnit, file
= "getGenGammaCDF.RK.txt")
115 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 evenlylogarithmicallyspaced 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 typeparameters frequently used in the ParaMonte librar...
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in CFortran Interoperati...
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in CFortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in CFortran Intero...
integer, parameter RKS
The singleprecision real kind in Fortran mode. On most platforms, this is an 32bit real kind.
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort fpp standardsemantics 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 /standardsemantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran cpp ffreelinelengthnone O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example output ⛓
53+0.682689488,
+0.499022126,
+0.346280664,
+0.229651660,
+0.146336332
60+0.112462923,
+0.800254866E1,
+0.116214290,
+0.297623754,
+0.788579822
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
15xlab = {
"CK" :
"X ( real/imaginary components )"
16 ,
"IK" :
"X ( integervalued )"
17 ,
"RK" :
"X ( realvalued )"
19legends = [
"$\kappa, 1/\omega, 1/\sigma = 1.0, 0.5, 0.5$"
20 ,
"$\kappa, 1/\omega, 1/\sigma = 2.0, 0.5, 1.0$"
21 ,
"$\kappa, 1/\omega, 1/\sigma = 0.5, 2.0, 0.5$"
22 ,
"$\kappa, 1/\omega, 1/\sigma = 0.2, 5.0, 0.2$"
23 ,
"$\kappa, 1/\omega, 1/\sigma = .14, 7.0, .14$"
24 ,
"$\kappa, 1/\omega, 1/\sigma = 2.0, 5.0, 0.3$"
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]
60 plt.xticks(fontsize = fontsize  2)
61 plt.yticks(fontsize = fontsize  2)
62 ax.set_xlabel(xlab[kind], fontsize = 17)
63 ax.set_ylabel(
"Cumulative Distribution Function (CDF)", fontsize = 17)
66 plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"")
67 ax.tick_params(axis =
"y", which =
"minor")
68 ax.tick_params(axis =
"x", which =
"minor")
70 plt.savefig(fileList[0].replace(
".txt",
".png"))
72 elif len(fileList) > 1:
74 sys.exit(
"Ambiguous file list exists.")
Visualization of the example output ⛓
 Test:
 test_pm_distGenGamma
 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 952 of file pm_distGenGamma.F90.