mo_moment Module Reference

Statistical moments. More...

Data Types
interface	absdev
	Mean absolute deviation from mean. More...
interface	average
	Mean of vector. More...
interface	central_moment
	R-central moment. More...
interface	central_moment_var
	R-central moment variance. More...
interface	correlation
	Correlation between two vectors. More...
interface	covariance
	Covariance between vectors. More...
interface	kurtosis
	Kurtosis of a vector. More...
interface	mean
	Mean of a vector. More...
interface	mixed_central_moment
	R-s mixed central moment between vectors. More...
interface	mixed_central_moment_var
	Mixed central moment variance. More...
interface	moment
	First four moments, stddev and mean absolute devation. More...
interface	skewness
	Skewness of a vector. More...
interface	stddev
	Standard deviation of a vector. More...
interface	variance
	Standard deviation of a vector. More...

Functions/Subroutines
real(dp) function	absdev_dp (dat, mask)
real(sp) function	absdev_sp (dat, mask)
real(dp) function	average_dp (dat, mask)
real(sp) function	average_sp (dat, mask)
real(dp) function	central_moment_dp (x, r, mask)
real(sp) function	central_moment_sp (x, r, mask)
real(dp) function	central_moment_var_dp (x, r, mask)
real(sp) function	central_moment_var_sp (x, r, mask)
real(dp) function	correlation_dp (x, y, mask)
real(sp) function	correlation_sp (x, y, mask)
real(dp) function	covariance_dp (x, y, mask)
real(sp) function	covariance_sp (x, y, mask)
real(dp) function	kurtosis_dp (dat, mask)
real(sp) function	kurtosis_sp (dat, mask)
real(dp) function	mean_dp (dat, mask)
real(sp) function	mean_sp (dat, mask)
	Mean of a vector.
real(dp) function	mixed_central_moment_dp (x, y, r, s, mask)
real(sp) function	mixed_central_moment_sp (x, y, r, s, mask)
real(dp) function	mixed_central_moment_var_dp (x, y, r, s, mask)
real(sp) function	mixed_central_moment_var_sp (x, y, r, s, mask)
subroutine	moment_dp (dat, average, variance, skewness, kurtosis, mean, stddev, absdev, mask, sample)
subroutine	moment_sp (dat, average, variance, skewness, kurtosis, mean, stddev, absdev, mask, sample)
real(dp) function	stddev_dp (dat, mask)
real(sp) function	stddev_sp (dat, mask)
real(dp) function	skewness_dp (dat, mask)
real(sp) function	skewness_sp (dat, mask)
real(dp) function	variance_dp (dat, mask)
real(sp) function	variance_sp (dat, mask)

Detailed Description

Statistical moments.

This module contains routines for the masked calculation of statistical properties such as moments and mixed moments of input vectors

Note

all except variance and standard deviation are population and not sample moments, i.e. they are normally divided by n and not (n-1)

Literature

Central moments and error variances LH Benedict & RD Gould, Towards better uncertainty estimates for turbulence statistics, Experiments in Fluids 22, 129-136, 1996

Changelog

• Matthias Cuntz, Nov 2011
  • written
• Matthias Cuntz, Dec 2011
  • mod. correlation, covariance
• M. Schroen, Sep 2015
  • average/mean for single value
• S. Mueller, Dec 2019
  • remove citations for common sence

Copyright

Copyright 2005-2024, the CHS Developers, Sabine Attinger: All rights reserved. FORCES is released under the LGPLv3+ license

The UFZ (CHS) FORCES code is free software. You can redistribute it and/or modify it under the terms of the GNU General Public License as published by the free Software Foundation either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You received a copy of the GNU Lesser General Public License along with the UFZ CHS FORCES code. It can be found in the files COPYING and COPYING.LESSER provided with this software. The complete GNU license text can also be found at http://www.gnu.org/licenses/.

Function/Subroutine Documentation

absdev_dp()

real(dp) function mo_moment::absdev_dp ( real(dp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 618 of file mo_moment.f90.

absdev_sp()

real(sp) function mo_moment::absdev_sp ( real(sp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 649 of file mo_moment.f90.

average_dp()

real(dp) function mo_moment::average_dp ( real(dp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 681 of file mo_moment.f90.

average_sp()

real(sp) function mo_moment::average_sp ( real(sp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 707 of file mo_moment.f90.

central_moment_dp()

real(dp) function mo_moment::central_moment_dp ( real(dp), dimension(:), intent(in)  x, integer(i4), intent(in)  r, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 734 of file mo_moment.f90.

central_moment_sp()

real(sp) function mo_moment::central_moment_sp ( real(sp), dimension(:), intent(in)  x, integer(i4), intent(in)  r, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 773 of file mo_moment.f90.

central_moment_var_dp()

real(dp) function mo_moment::central_moment_var_dp ( real(dp), dimension(:), intent(in)  x, integer(i4), intent(in)  r, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 813 of file mo_moment.f90.

central_moment_var_sp()

real(sp) function mo_moment::central_moment_var_sp ( real(sp), dimension(:), intent(in)  x, integer(i4), intent(in)  r, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 851 of file mo_moment.f90.

correlation_dp()

real(dp) function mo_moment::correlation_dp ( real(dp), dimension(:), intent(in)  x, real(dp), dimension(:), intent(in)  y, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 890 of file mo_moment.f90.

correlation_sp()

real(sp) function mo_moment::correlation_sp ( real(sp), dimension(:), intent(in)  x, real(sp), dimension(:), intent(in)  y, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 925 of file mo_moment.f90.

covariance_dp()

real(dp) function mo_moment::covariance_dp ( real(dp), dimension(:), intent(in)  x, real(dp), dimension(:), intent(in)  y, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 961 of file mo_moment.f90.

covariance_sp()

real(sp) function mo_moment::covariance_sp ( real(sp), dimension(:), intent(in)  x, real(sp), dimension(:), intent(in)  y, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 993 of file mo_moment.f90.

kurtosis_dp()

real(dp) function mo_moment::kurtosis_dp ( real(dp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1026 of file mo_moment.f90.

kurtosis_sp()

real(sp) function mo_moment::kurtosis_sp ( real(sp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1067 of file mo_moment.f90.

mean_dp()

real(dp) function mo_moment::mean_dp ( real(dp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1109 of file mo_moment.f90.

mean_sp()

real(sp) function mo_moment::mean_sp ( real(sp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Mean of a vector.

Calculates the average value of a vector, i.e. the first moment of a series of numbers:

Note

Input values must be floating points.

Author

Matthias Cuntz

Date

Nov 2011

Definition at line 1136 of file mo_moment.f90.

Referenced by mo_moment::mean::mean_sp().

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mixed_central_moment_dp()

real(dp) function mo_moment::mixed_central_moment_dp ( real(dp), dimension(:), intent(in)  x, real(dp), dimension(:), intent(in)  y, integer(i4), intent(in)  r, integer(i4), intent(in)  s, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1164 of file mo_moment.f90.

mixed_central_moment_sp()

real(sp) function mo_moment::mixed_central_moment_sp ( real(sp), dimension(:), intent(in)  x, real(sp), dimension(:), intent(in)  y, integer(i4), intent(in)  r, integer(i4), intent(in)  s, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1214 of file mo_moment.f90.

mixed_central_moment_var_dp()

real(dp) function mo_moment::mixed_central_moment_var_dp ( real(dp), dimension(:), intent(in)  x, real(dp), dimension(:), intent(in)  y, integer(i4), intent(in)  r, integer(i4), intent(in)  s, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1265 of file mo_moment.f90.

mixed_central_moment_var_sp()

real(sp) function mo_moment::mixed_central_moment_var_sp ( real(sp), dimension(:), intent(in)  x, real(sp), dimension(:), intent(in)  y, integer(i4), intent(in)  r, integer(i4), intent(in)  s, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1311 of file mo_moment.f90.

moment_dp()

subroutine mo_moment::moment_dp ( real(dp), dimension(:), intent(in)  dat, real(dp), intent(out), optional  average, real(dp), intent(out), optional  variance, real(dp), intent(out), optional  skewness, real(dp), intent(out), optional  kurtosis, real(dp), intent(out), optional  mean, real(dp), intent(out), optional  stddev, real(dp), intent(out), optional  absdev, logical, dimension(:), intent(in), optional  mask, logical, intent(in), optional  sample  )

private

Definition at line 1358 of file mo_moment.f90.

moment_sp()

subroutine mo_moment::moment_sp ( real(sp), dimension(:), intent(in)  dat, real(sp), intent(out), optional  average, real(sp), intent(out), optional  variance, real(sp), intent(out), optional  skewness, real(sp), intent(out), optional  kurtosis, real(sp), intent(out), optional  mean, real(sp), intent(out), optional  stddev, real(sp), intent(out), optional  absdev, logical, dimension(:), intent(in), optional  mask, logical, intent(in), optional  sample  )

private

Definition at line 1435 of file mo_moment.f90.

skewness_dp()

real(dp) function mo_moment::skewness_dp ( real(dp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1588 of file mo_moment.f90.

skewness_sp()

real(sp) function mo_moment::skewness_sp ( real(sp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1630 of file mo_moment.f90.

stddev_dp()

real(dp) function mo_moment::stddev_dp ( real(dp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1513 of file mo_moment.f90.

stddev_sp()

real(sp) function mo_moment::stddev_sp ( real(sp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1550 of file mo_moment.f90.

variance_dp()

real(dp) function mo_moment::variance_dp ( real(dp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1673 of file mo_moment.f90.

variance_sp()

real(sp) function mo_moment::variance_sp ( real(sp), dimension(:), intent(in)  dat, logical, dimension(:), intent(in), optional  mask  )

private

Definition at line 1709 of file mo_moment.f90.