Return the CDF of the Beta distribution for the given parameters \((\alpha, \beta)\) as defined in the details section of pm_distBeta.
More...
Return the CDF of the Beta distribution for the given parameters \((\alpha, \beta)\) as defined in the details section of pm_distBeta.
- Parameters
-
[in] | cdf | : The output scalar (or array of the same shape as other array-like arguments) of the same type and kind as the input argument x containing the regularized Incomplete Beta Function. |
[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 value at which the function must be computed. |
[in] | alpha | : The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as x . |
[in] | beta | : The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as x . |
[in] | logFuncBeta | : The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as x , representing the natural logarithm of the Beta Function as returned by getLogBeta(alpha, beta).
Providing this argument can lead to significant runtime performance gains when the interface is called repeatedly for different x values but with identical alpha and beta . |
[in] | signed | : The input scalar (or array of the same shape as other array-like arguments) of type logical of default kind LK.
-
If
signed = .false. , the input x must be in range 0 <= x <= 1 and the output betaInc will be the expected incomplete Beta function in range 0 <= betaInc <= 1 .
-
If
signed = .true. , then the following rules hold:
-
If the condition
x < 0 holds, then the value x = 1 - x < 0 will be used instead of x .
-
If the output
betaInc is near 1 , the output will be returned as betaInc = betaInc - 1 < 0 instead of betaInc .
Therefore, the user is expected to be aware of and apply the necessary correction (addition by 1 ) before using the output value.
Specifying signed = .true. can lead to considerably more accurate calculations (by orders of magnitudes) for values of x and betaInc that are near 1 .
The loss of precision near 1 occurs because of inadequate resolution of real number representations in digital computers near 1 which is orders of magnitude worse than the precision near 0 .
|
[out] | info | : The output scalar (or array of the same shape as other array-like arguments) of type integer of default kind IK.
It is 0 if and only if the computation converges, otherwise, it is set to a non-zero integer whose value depends on the root cause of the lack of convergence.
Convergence typically fails if alpha or beta are too large.
For more information, see the corresponding argument of setBetaInc.
|
- Returns
Possible calling interfaces ⛓
call setBetaCDF(cdf, x, alpha, beta, logFuncBeta, signed, info)
Return the CDF of the Beta distribution for the given parameters as defined in the details section o...
This module contains classes and procedures for computing various statistical quantities related to t...
- Warning
- All warnings associated with setBetaInc also apply to the procedures of this generic interface.
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
- getLogBeta
setBetaCDF
setBetaRand
getBetaLogPDF
Example usage ⛓
13 integer(IK) :: info(
4)
14 type(display_type) :: disp
20 call disp%show(
"call setBetaCDF(cdf(1), x = 0._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))")
21 call setBetaCDF(cdf(
1), x
= 0._RKG, alpha
= 2._RKG, beta
= 3._RKG, logFuncBeta
= getLogBeta(
2._RKG,
3._RKG), signed
= signed, info
= info(
1))
22 call disp%show(
"if (info(1) /= 0) error stop")
23 if (info(
1)
/= 0)
error stop
29 call disp%show(
"call setBetaCDF(cdf(1), x = .5_RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))")
30 call setBetaCDF(cdf(
1), x
= .
5_RKG, alpha
= 2._RKG, beta
= 3._RKG, logFuncBeta
= getLogBeta(
2._RKG,
3._RKG), signed
= signed, info
= info(
1))
31 call disp%show(
"if (info(1) /= 0) error stop")
32 if (info(
1)
/= 0)
error stop
38 call disp%show(
"call setBetaCDF(cdf(1), x = 1._RKG, alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info(1))")
39 call setBetaCDF(cdf(
1), x
= 1._RKG, alpha
= 2._RKG, beta
= 3._RKG, logFuncBeta
= getLogBeta(
2._RKG,
3._RKG), signed
= signed, info
= info(
1))
40 call disp%show(
"if (info(1) /= 0) error stop")
41 if (info(
1)
/= 0)
error stop
47 call disp%show(
"call setBetaCDF(cdf, x = [0._RKG, 0.1_RKG, 0.5_RKG, 1._RKG], alpha = 2._RKG, beta = 3._RKG, logFuncBeta = getLogBeta(2._RKG, 3._RKG), signed = signed, info = info)")
48 call setBetaCDF(cdf, x
= [
0._RKG,
0.1_RKG,
0.5_RKG,
1._RKG], alpha
= 2._RKG, beta
= 3._RKG, logFuncBeta
= getLogBeta(
2._RKG,
3._RKG), signed
= signed, info
= info)
49 call disp%show(
"if (any(info /= 0)) error stop")
50 if (
any(info
/= 0))
error stop
56 call disp%show(
"call setBetaCDF(cdf, x = [0._RKG, .1_RKG, 0.5_RKG, 1._RKG], alpha = [0.1_RKG, .5_RKG, 1._RKG, 10._RKG], beta = 3._RKG, logFuncBeta = getLogBeta([0.1_RKG, .5_RKG, 1._RKG, 10._RKG], 3._RKG), signed = signed, info = info)")
57 call setBetaCDF(cdf, x
= [
0._RKG, .
1_RKG,
0.5_RKG,
1._RKG], alpha
= [
0.1_RKG, .
5_RKG,
1._RKG,
10._RKG], beta
= 3._RKG, logFuncBeta
= getLogBeta([
0.1_RKG, .
5_RKG,
1._RKG,
10._RKG],
3._RKG), signed
= signed, info
= info)
58 call disp%show(
"if (any(info /= 0)) error stop")
59 if (
any(info
/= 0))
error stop
71 integer(IK) ,
parameter :: NP
= 1000_IK
72 real(RKG) :: cdf(
4), X(NP)
73 integer :: fileUnit, i
76 open(newunit
= fileUnit, file
= "setBetaCDF.RK.txt")
78 call setBetaCDF(cdf, X(i), [.
5_RKG,
5._RKG, .
5_RKG,
5._RKG], [.
5_RKG,
1.0_RKG,
5.0_RKG,
10._RKG],
getLogBeta([.
5_RKG,
5._RKG, .
5_RKG,
5._RKG], [.
5_RKG,
1.0_RKG,
5.0_RKG,
10._RKG]), signed
= signed, info
= info)
79 if (
any(info
/= 0))
error stop
80 write(fileUnit,
"(*(g0,:,' '))") X(i), cdf
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
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.
Generate and return the natural logarithm of the Beta Function as defined in the details section of ...
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...
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
This module contains classes and procedures for computing the mathematical Beta Function and its inve...
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 ⛓
2call setBetaCDF(cdf(
1), x
= 0._RKG, alpha
= 2._RKG, beta
= 3._RKG, logFuncBeta
= getLogBeta(
2._RKG,
3._RKG), signed
= signed, info
= info(
1))
3if (info(
1)
/= 0)
error stop
5+0.00000000000000000000000000000000000
8call setBetaCDF(cdf(
1), x
= .
5_RKG, alpha
= 2._RKG, beta
= 3._RKG, logFuncBeta
= getLogBeta(
2._RKG,
3._RKG), signed
= signed, info
= info(
1))
9if (info(
1)
/= 0)
error stop
11+0.687500000000000000000000000000000096
14call setBetaCDF(cdf(
1), x
= 1._RKG, alpha
= 2._RKG, beta
= 3._RKG, logFuncBeta
= getLogBeta(
2._RKG,
3._RKG), signed
= signed, info
= info(
1))
15if (info(
1)
/= 0)
error stop
17+1.00000000000000000000000000000000000
20call setBetaCDF(cdf, x
= [
0._RKG,
0.1_RKG,
0.5_RKG,
1._RKG], alpha
= 2._RKG, beta
= 3._RKG, logFuncBeta
= getLogBeta(
2._RKG,
3._RKG), signed
= signed, info
= info)
21if (
any(info
/= 0))
error stop
23+0.00000000000000000000000000000000000,
+0.522999999999999999999999999999999659E-1,
+0.687500000000000000000000000000000096,
+1.00000000000000000000000000000000000
26call setBetaCDF(cdf, x
= [
0._RKG, .
1_RKG,
0.5_RKG,
1._RKG], alpha
= [
0.1_RKG, .
5_RKG,
1._RKG,
10._RKG], beta
= 3._RKG, logFuncBeta
= getLogBeta([
0.1_RKG, .
5_RKG,
1._RKG,
10._RKG],
3._RKG), signed
= signed, info
= info)
27if (
any(info
/= 0))
error stop
29+0.00000000000000000000000000000000000,
+0.554584444652029525349305955354888178,
+0.875000000000000000000000000000000000,
+1.00000000000000000000000000000000000
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
12label = [
r"$\alpha, \beta = .5, 0.5$"
13 ,
r"$\alpha, \beta = 5., 1.0$"
14 ,
r"$\alpha, \beta = .5, 5.0$"
15 ,
r"$\alpha, \beta = 5., 10.$"
18pattern =
"*." + kind +
".txt"
19fileList = glob.glob(pattern)
22 df = pd.read_csv(fileList[0], delimiter =
" ")
24 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
27 for i
in range(1,len(df.values[0,:]+1)):
29 plt.plot( df.values[:, 0]
34 plt.xticks(fontsize = fontsize - 2)
35 plt.yticks(fontsize = fontsize - 2)
36 ax.set_xlabel(
"x", fontsize = fontsize)
37 ax.set_ylabel(
"Beta CDF", fontsize = fontsize)
39 plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"-")
40 ax.tick_params(axis =
"y", which =
"minor")
41 ax.tick_params(axis =
"x", which =
"minor")
49 plt.savefig(fileList[0].replace(
".txt",
".png"))
53 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 881 of file pm_distBeta.F90.