Generate and return the Cumulative Distribution Function (CDF) of the univariate Normal distribution.
More...
Generate and return the Cumulative Distribution Function (CDF) of the univariate Normal distribution.
 Parameters

[in]  x  : The input scalar or array of the same shape as other arraylike arguments, of the same type and kind as the output cdf , representing the point(s) at which the CDF must be computed. 
[in]  mu  : The input scalar or array of the same shape as other arraylike arguments of the same type and kind as the output cdf representing the location parameter of the distribution.
(optional, default = 0 ) 
[in]  sigma  : The input scalar of the same type and kind as the output cdf representing the scale parameter of the distribution.
(optional, default = 1. ) 
 Returns
cdf
: The output scalar or array of the same shape as the input arraylike arguments, of,

type
real
of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the CDF of the distribution at the specified input x
.
Possible calling interfaces ⛓
Generate and return the Cumulative Distribution Function (CDF) of the univariate Normal distribution.
This module contains classes and procedures for computing various statistical quantities related to t...
 Warning
 The condition
0. < sigma
must hold for the corresponding procedure argument.
This condition is 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
 setNormCDF
Example usage ⛓
12 integer(IK),
parameter :: NP
= 1000_IK
13 real(RK), dimension(NP) :: Point, mu, Sigma, CDF
15 type(display_type) :: disp
20 call setLogSpace(Sigma, logx1
= log(
0.1_RK), logx2
= log(
10._RK))
23 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
24 call disp%show(
"! Compute the Cumulative Distribution Function (CDF) of the (Standard) Normal distribution.")
25 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
37 call disp%show(
"CDF(1) = getNormCDF(Point(NP/2))")
54 call disp%show(
"CDF(1) = getNormCDF(Point(1), mu(1))")
61 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
62 call disp%show(
"! CDF with a standard deviation.")
63 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
71 call disp%show(
"CDF(1) = getNormCDF(Point(1), Sigma(1))")
78 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
79 call disp%show(
"! CDF with a mean and a standard deviation.")
80 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
90 call disp%show(
"CDF(1) = getNormCDF(Point(1), mu(1), Sigma(1))")
97 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
98 call disp%show(
"! A vector of CDF at different points with the same mean and standard deviation.")
99 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
109 call disp%show(
"CDF(1:NP:NP/5) = getNormCDF(Point(1:NP:NP/5), mu(1), Sigma(1))")
110 CDF(
1:NP:NP
/5)
= getNormCDF(Point(
1:NP:NP
/5), mu(
1), Sigma(
1))
116 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
117 call disp%show(
"! A vector of CDF at the same point but with different means and standard deviations.")
118 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
128 call disp%show(
"CDF(1:NP:NP/5) = getNormCDF(Point(1), mu(1:NP:NP/5), Sigma(1:NP:NP/5))")
129 CDF(
1:NP:NP
/5)
= getNormCDF(Point(
1), mu(
1:NP:NP
/5), Sigma(
1:NP:NP
/5))
135 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
136 call disp%show(
"! A vector of CDF at different points with different means and a standard deviations.")
137 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
147 call disp%show(
"CDF(1:NP:NP/5) = getNormCDF(Point(1:NP:NP/5), mu(1:NP:NP/5), Sigma(1:NP:NP/5))")
148 CDF(
1:NP:NP
/5)
= getNormCDF(Point(
1:NP:NP
/5), mu(
1:NP:NP
/5), Sigma(
1:NP:NP
/5))
158 integer(IK) :: fileUnit, i
159 open(newunit
= fileUnit, file
= "getNormCDF.RK.txt")
160 write(fileUnit,
"(5(g0,:,' '))") (Point(i),
getNormCDF(Point(i), [
0._RK,
0._RK,
0._RK,
2._RK], sigma
= [
3.0_RK,
1.0_RK,
0.3_RK,
1.0_RK]), i
= 1, NP)
Return the linSpace output argument with size(linSpace) elements of evenlyspaced values over the int...
Return the logSpace output argument with size(logSpace) elements of logarithmicallyevenlyspaced val...
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...
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 ⛓
130.10010010010010006E1
30+0.28665157186802404E6
7310.000000000000000,
5.9959959959959956,
1.9919919919919913,
+2.0120120120120113,
+6.0160160160160174
74CDF(
1:NP:NP
/5)
= getNormCDF(Point(
1:NP:NP
/5), mu(
1), Sigma(
1))
76+0.0000000000000000,
+0.0000000000000000,
+1.0000000000000000,
+1.0000000000000000,
+1.0000000000000000
855.0000000000000000,
2.9979979979979978,
0.99599599599599564,
+1.0060060060060056,
+3.0080080080080087
87+0.10000000000000003,
+0.25142033481427983,
+0.63212184758124557,
+1.5892828656229783,
+3.9957803018952722
90CDF(
1:NP:NP
/5)
= getNormCDF(Point(
1), mu(
1:NP:NP
/5), Sigma(
1:NP:NP
/5))
92+0.0000000000000000,
+0.0000000000000000,
+0.0000000000000000,
+0.21777024628022446E11,
+0.56609157067133431E3
1015.0000000000000000,
2.9979979979979978,
0.99599599599599564,
+1.0060060060060056,
+3.0080080080080087
103+0.10000000000000003,
+0.25142033481427983,
+0.63212184758124557,
+1.5892828656229783,
+3.9957803018952722
10510.000000000000000,
5.9959959959959956,
1.9919919919919913,
+2.0120120120120113,
+6.0160160160160174
106CDF(
1:NP:NP
/5)
= getNormCDF(Point(
1:NP:NP
/5), mu(
1:NP:NP
/5), Sigma(
1:NP:NP
/5))
108+0.0000000000000000,
+0.0000000000000000,
+0.57554482194544898E1,
+0.73663111418286575,
+0.77421378819753417
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
16xlab = {
"CK" :
"X ( real/imaginary components )"
17 ,
"IK" :
"X ( integervalued )"
18 ,
"RK" :
"X ( realvalued )"
20legends = [
r"$\mu = 0.0,~\sigma = 3.0$"
21 ,
r"$\mu = 0.0,~\sigma = 1.0$"
22 ,
r"$\mu = 0.0,~\sigma = 0.3$"
23 ,
r"$\mu = 2.,~\sigma = 1.0$"
26for kind
in [
"IK",
"CK",
"RK"]:
28 pattern =
"*." + kind +
".txt"
29 fileList = glob.glob(pattern)
30 if len(fileList) == 1:
32 df = pd.read_csv(fileList[0], delimiter =
" ")
34 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
38 plt.plot( df.values[:, 0]
41 , linewidth = linewidth
44 plt.plot( df.values[:, 1]
47 , linewidth = linewidth
51 plt.plot( df.values[:, 0]
54 , linewidth = linewidth
61 plt.xticks(fontsize = fontsize  2)
62 plt.yticks(fontsize = fontsize  2)
63 ax.set_xlabel(xlab[kind], fontsize = 17)
64 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_distNorm
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 754 of file pm_distNorm.F90.