Return a scalar or array of arbitrary rank of Beta-distributed random values in range \([0, 1]\) (or \((0, 1)\), depending on the specific parameter values) with the specified two shape parameters \((\alpha, \beta)\) of the Beta distribution corresponding to the procedure arguments (alpha, beta)
.
More...
Return a scalar or array of arbitrary rank of Beta-distributed random values in range \([0, 1]\) (or \((0, 1)\), depending on the specific parameter values) with the specified two shape parameters \((\alpha, \beta)\) of the Beta distribution corresponding to the procedure arguments (alpha, beta)
.
See the documentation of pm_distBeta for more information on the Probability Density Function (PDF) of the Beta distribution and RNG.
- Parameters
-
[in,out] | rng | : The input/output scalar that can be an object of,
-
type rngf_type, implying the use of intrinsic Fortran uniform RNG.
-
type xoshiro256ssw_type, implying the use of xoshiro256** uniform RNG.
(optional, default = rngf_type, implying the use of the intrinsic Fortran URNG.) |
[out] | rand | : The output scalar or
-
array of rank
1 , or
-
array of arbitrary rank if the
rng argument is missing or set to rngf_type, or
of,
-
type
real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128).
On output, it contains Beta-distributed random value(s).
|
[in] | alpha | : The input scalar or array of the same shape as other array-like arguments, of the same type and kind as rand , containing the first shape parameter of the distribution.
|
[in] | beta | : The input scalar or array of the same shape as other array-like arguments, of the same type and kind as rand , containing the second shape parameter of the distribution.
|
Possible calling interfaces ⛓
Return a scalar or array of arbitrary rank of Beta-distributed random values in range (or ,...
This module contains classes and procedures for computing various statistical quantities related to t...
- Warning
- The conditions \(0. < \alpha\) and \(0. < \beta\) must hold for the input arguments
(alpha, beta)
.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1
.
- Note
- For repeated Beta RNG with fixed
alpha
, it is best to pass a vector of rand
to be filled with random numbers rather than calling the procedures with scalar rand
argument repeatedly.
In addition to avoiding procedure call overhead, vectorized RGN in this particular case also avoids an unnecessary division and square-root operation.
- See also
- getBetaLogPDF
setBetaLogPDF
getBetaCDF
setBetaCDF
Example usage ⛓
13 type(xoshiro256ssw_type) :: rng
14 integer(IK),
parameter :: NP
= 1000_IK
15 real(RKG), dimension(NP) :: alpha, beta, rand
17 type(display_type) :: disp
20 call setLogSpace(alpha, logx1
= log(
0.1_RKG), logx2
= log(
10._RKG))
21 call setLogSpace(beta, logx1
= log(
0.1_RKG), logx2
= log(
10._RKG))
24 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
25 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
26 call disp%show(
"! Generate random numbers from the Beta distribution.")
27 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
28 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
36 call disp%show(
"call setBetaRand(rand(1), 1._RKG, beta = beta(1))")
47 call disp%show(
"rng = xoshiro256ssw_type()")
49 call disp%show(
"call setBetaRand(rng, rand(1:2), 1._RKG, beta = beta(1))")
50 call setBetaRand(rng, rand(
1:
2),
1._RKG, beta
= beta(
1))
60 call disp%show(
"call setBetaRand(rand(1:2), alpha(1), beta = beta(1))")
61 call setBetaRand(rand(
1:
2), alpha(
1), beta
= beta(
1))
71 call disp%show(
"call setBetaRand(rand(1:NP:NP/3), alpha(1:NP:NP/3), beta = beta(1:NP:NP/3))")
72 call setBetaRand(rand(
1:NP:NP
/3), alpha(
1:NP:NP
/3), beta
= beta(
1:NP:NP
/3))
83 real(RKG) :: rand(
5000,
4)
84 call setBetaRand(rand(:,
1), alpha
= 0.5_RKG, beta
= 0.5_RKG)
85 call setBetaRand(rand(:,
2), alpha
= 2.0_RKG, beta
= 2.0_RKG)
86 call setBetaRand(rand(:,
3), alpha
= 2.0_RKG, beta
= 5.0_RKG)
87 call setBetaRand(rand(:,
4), alpha
= 5.0_RKG, beta
= 2.0_RKG)
88 if (
0 /= getErrTableWrite(SK_
"setBetaRand.RK.txt", rand))
error stop "Failed to write table."
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
Return the logSpace output argument with size(logSpace) elements of logarithmically-evenly-spaced val...
Generate and return the iostat code resulting from writing the input table of rank 1 or 2 to the spec...
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 computing various statistical quantities related to t...
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 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.
This is the derived type for declaring and generating objects of type xoshiro256ssw_type containing a...
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 ⛓
23call setBetaRand(rng, rand(
1:
2),
1._RKG, beta
= beta(
1))
25+0.999997199,
+0.600171797E-1
32call setBetaRand(rand(
1:
2), alpha(
1), beta
= beta(
1))
34+0.141968787,
+0.999999702
38+0.999999940E-1,
+0.464158833,
+2.15443444,
+10.0000010
40+0.999999940E-1,
+0.464158833,
+2.15443444,
+10.0000010
41call setBetaRand(rand(
1:NP:NP
/3), alpha(
1:NP:NP
/3), beta
= beta(
1:NP:NP
/3))
43+0.662140606E-3,
+0.850791335E-1,
+0.814989626,
+0.523548245
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
16xlab = {
"CK" :
"Beta Random Value ( real/imaginary components )"
17 ,
"IK" :
"Beta Random Value ( integer-valued )"
18 ,
"RK" :
"Beta Random Value ( real-valued )"
20legends = [
r"$\alpha = 0.5, \beta = 0.5$"
21 ,
r"$\alpha = 2.0, \beta = 2.0$"
22 ,
r"$\alpha = 2.0, \beta = 5.0$"
23 ,
r"$\alpha = 5.0, \beta = 2.0$"
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 =
",", header =
None)
34 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
37 for j
in range(len(df.values[0,:])):
39 plt.hist( df.values[:,j]
40 , histtype =
"stepfilled"
45 plt.hist( df.values[:,j]
46 , histtype =
"stepfilled"
53 plt.xticks(fontsize = fontsize - 2)
54 plt.yticks(fontsize = fontsize - 2)
55 ax.set_xlabel(xlab[kind], fontsize = 17)
56 ax.set_ylabel(
"Count", fontsize = 17)
57 ax.set_title(
"Histograms of {} Beta random values".format(len(df.values[:, 0])), fontsize = 17)
59 plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"-")
60 ax.tick_params(axis =
"y", which =
"minor")
61 ax.tick_params(axis =
"x", which =
"minor")
63 plt.savefig(fileList[0].replace(
".txt",
".png"))
65 elif len(fileList) > 1:
67 sys.exit(
"Ambiguous file list exists.")
Visualization of the example output ⛓
- Test:
- test_pm_distBeta
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 1039 of file pm_distBeta.F90.