Generate and return the Normal Quantile corresponding to the input CDF of the univariate Normal distribution.
More...
Generate and return the Normal Quantile corresponding to the input CDF of the univariate Normal distribution.
- Parameters
-
[in] | cdf | : The input scalar or array of the same shape as other array-like arguments, of the same type and kind as the output quantile , representing the point(s) (probabilities) at which the quantile must be computed. The cdf must be in the range \([0, 1]\).
|
[in] | mu | : The input scalar or array of the same shape as other array-like arguments of the same type and kind as the output quantile representing the location parameter of the distribution.
(optional, default = 0 ) |
[in] | sigma | : The input scalar of the same type and kind as the output quantile , representing the scale parameter of the distribution.
(optional, default = 1. ) |
- Returns
quantile
: The output scalar or array of the same shape as the input array-like arguments, of,
-
type
real
of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the quantile of the distribution at the specified input cdf
.
Possible calling interfaces ⛓
Generate and return the Normal Quantile corresponding to the input CDF of the univariate Normal distr...
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 arguments.
The condition 0. <= cdf .and. cdf <= 1.
must hold for the corresponding procedure 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
- setNormQuan
Example usage ⛓
10 real,
allocatable :: cdf(:), quantile(:), mu(:), sigma(:)
12 type(display_type) :: disp
16 call disp%show(
"cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]")
17 cdf
= [
0.,
0.05,
0.158655,
0.5,
0.658655,
0.95,
1.]
18 call disp%show(
"quantile = getNormQuan(cdf)")
25 call disp%show(
"cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]")
26 cdf
= [
0.,
0.05,
0.158655,
0.5,
0.658655,
0.95,
1.]
27 call disp%show(
"quantile = getNormQuan(cdf, mu = 1.)")
34 call disp%show(
"cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]")
35 cdf
= [
0.,
0.05,
0.158655,
0.5,
0.658655,
0.95,
1.]
36 call disp%show(
"quantile = getNormQuan(cdf, mu = 1., sigma = 10.)")
47 integer(IK) :: fileUnit, i
48 open(newunit
= fileUnit, file
= "getNormQuan.RK.txt")
49 cdf
= getLinSpace(
0.,
1., count
= 1000_IK, lopen
= .true._LK, fopen
= .true._LK)
51 write(fileUnit,
"(5(g0,:,','))") cdf(i),
getNormQuan(cdf(i), [
0.,
0.,
0.,
-2.], sigma
= [
3.,
1.,
0.3,
1.])
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
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 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...
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 ⛓
2cdf
= [
0.,
0.05,
0.158655,
0.5,
0.658655,
0.95,
1.]
5-0.340282347E+39,
-1.64485335,
-1.00000107,
+0.00000000,
+0.408795118,
+1.64485335,
+0.340282347E+39
8cdf
= [
0.,
0.05,
0.158655,
0.5,
0.658655,
0.95,
1.]
11-0.340282347E+39,
-0.644853354,
-0.107288361E-5,
+1.00000000,
+1.40879512,
+2.64485335,
+0.340282347E+39
14cdf
= [
0.,
0.05,
0.158655,
0.5,
0.658655,
0.95,
1.]
17-0.340282347E+39,
-15.4485340,
-9.00001049,
+1.00000000,
+5.08795118,
+17.4485340,
+0.340282347E+39
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
16xlab = {
"CK" :
"CDF ( real/imaginary components )"
17 ,
"IK" :
"CDF ( integer-valued )"
18 ,
"RK" :
"CDF ( real-valued )"
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(
"Quantile Function (ICDF)", 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 1138 of file pm_distNorm.F90.