Return a scalar (or array of arbitrary rank) of the natural logarithm(s) of random value(s) from the (Truncated) Pareto distribution with parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\).
More...
Return a scalar (or array of arbitrary rank) of the natural logarithm(s) of random value(s) from the (Truncated) Pareto distribution with parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\).
See the documentation of pm_distPareto for more information on generating random numbers from the (Truncated) Pareto distribution.
- Parameters
-
[out] | logRand | : The output scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha , containing the random value(s) from the specified distribution.
|
[in] | negExpRand | : The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha , containing a random value from the standard Negative Exponential distribution ( \(\mu = 0, \sigma = 1.\)).
This argument can be readily obtained by calling getNegExpRand(sigma = 1.).
|
[in] | alpha | : The input scalar (or array of the same rank, shape, and size as other array like arguments), of
-
type
real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the shape parameter ( \(\alpha\)) of the distribution.
|
[in] | logMinX | : The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha , containing the natural logarithm of the first scale parameter of the distribution, representing the minimum of the support of the distribution.
|
[in] | logCDFNF | : The input scalar (or array of the same rank, shape, and size as other array like arguments), of the same type and kind as alpha , containing the natural logarithm of the normalization factor of the CDF of the (Truncated) Pareto distribution.
Specifying this argument when calling this procedure repeatedly with fixed \((\alpha, x_\mathrm{min}, x_\mathrm{max})\) parameters will significantly improve the runtime performance.
This argument can be readily obtained by calling getParetoLogCDFNF(alpha, logMinX, logMaxX).
(optional, default = getParetoLogCDFNF(alpha, logMinX, logMaxX). If present, it implies a (Truncated) Pareto distribution.) |
Possible calling interfaces ⛓
!
Return a scalar (or array of arbitrary rank) of the natural logarithm(s) of random value(s) from the ...
This module contains classes and procedures for computing various statistical quantities related to t...
- Warning
- The condition
alpha < 0
must hold for the corresponding input arguments.
The condition negExpRand <= 0
must hold for the corresponding input 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
- getParetoLogRand
Example usage ⛓
13 type(display_type) :: disp
17 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
18 call disp%show(
"! Compute random value(s) from the Pareto distribution.")
19 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
23 call disp%show(
"call setParetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2.) ! Pareto distribution.")
30 call disp%show(
"call setParetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2.) ! Pareto distribution.")
37 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
38 call disp%show(
"! Compute random value(s) from the Truncated Pareto distribution.")
39 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
43 call disp%show(
"call setParetoLogRand(logx(1), negExpRand = getNegExpRand(1.), alpha = -2., logMinX = -2., logCDFNF = getParetoLogCDFNF(alpha = -2., logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.")
50 call disp%show(
"call setParetoLogRand(logx(1:3), negExpRand = getNegExpRand([1., 1., 1.]), alpha = -[+2., +3., +4.], logMinX = -2., logCDFNF = getParetoLogCDFNF(alpha = -[+2., +3., +4.], logMinX = -2., logMaxX = 5.)) ! Truncated Pareto distribution.")
51 call setParetoLogRand(logx(
1:
3), negExpRand
= getNegExpRand([
1.,
1.,
1.]), alpha
= -[
+2.,
+3.,
+4.], logMinX
= -2., logCDFNF
= getParetoLogCDFNF(alpha
= -[
+2.,
+3.,
+4.], logMinX
= -2., logMaxX
= 5.))
62 real :: alpha(
3), logMinX(
3), logMaxX(
3), logx(
3)
63 integer(IK) :: fileUnit, i
64 alpha
= -[.
5,
1.,
10.]
65 logMinX
= log([
3.,
1.,
2.])
66 logMaxX
= log([
5.,
4.,
huge(
0.)])
67 open(newunit
= fileUnit, file
= "setParetoLogRand.RK.txt")
71 write(fileUnit,
"(*(g0,:,', '))")
exp(logx)
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
Return a scalar (or array of arbitrary rank of) random value(s) from the Negative Exponential distrib...
Generate and return the natural logarithm of the normalization factor of the CDF of the (Truncated) P...
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 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 ⛓
14-1.91962278,
-1.77407873,
-1.42170680
27call setParetoLogRand(logx(
1:
3), negExpRand
= getNegExpRand([
1.,
1.,
1.]), alpha
= -[
+2.,
+3.,
+4.], logMinX
= -2., logCDFNF
= getParetoLogCDFNF(alpha
= -[
+2.,
+3.,
+4.], logMinX
= -2., logMaxX
= 5.))
29-1.94168150,
-1.98973334,
-1.86360693
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
16xlab = {
"CK" :
"Random Value ( Real / Imaginary ))"
17 ,
"IK" :
"Random Value ( Integer )"
18 ,
"RK" :
"Random Value ( Real )"
20legends = [
r"$\alpha = -.5, x_{min} = +3., x_{max} = +5$"
21 ,
r"$\alpha = -1., x_{min} = +1., x_{max} = +4$"
22 ,
r"$\alpha = -10, x_{min} = +2., x_{max} = +\infty$"
25for kind
in [
"IK",
"CK",
"RK"]:
27 pattern =
"*." + kind +
".txt"
28 fileList = glob.glob(pattern)
29 if len(fileList) == 1:
31 df = pd.read_csv(fileList[0], delimiter =
", ")
33 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
37 ax.hist ( df.values[:, 0]
39 , histtype =
"stepfilled"
43 ax.hist ( df.values[:, 1]
45 , histtype =
"stepfilled"
50 ax.hist ( df.values[:,:]
52 , histtype =
"stepfilled"
56 ax.legend ( 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(
"Density", fontsize = 17)
64 ax.set_title(
"Histogram of {} randomly generated values".format(len(df.values)), fontsize = fontsize)
68 plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"-")
69 ax.tick_params(axis =
"y", which =
"minor")
70 ax.tick_params(axis =
"x", which =
"minor")
71 ax.set_axisbelow(
True)
74 plt.savefig(fileList[0].replace(
".txt",
".png"))
76 elif len(fileList) > 1:
78 sys.exit(
"Ambiguous file list exists.")
Visualization of the example output ⛓
- Test:
- test_pm_distPareto
- Todo:
- Critical Priority: This interface can be extended to support vector-like
logRand
arguments other than the elemental
approach.
Such an extension would be sensible only if the new interface improves the performance against the elemental
approach.
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 1925 of file pm_distPareto.F90.