L-Moment Algorithms in Python

## Project Description

"""

This library was designed to use L-moments to predict optimal parameters

for a number of distributions. Distributions supported in this file are

listed below, with their distribution suffix:

*Exponential (EXP)

*Gamma (GAM)

*Generalised Extreme Value (GEV)

*Generalised Logistic (GLO)

*Generalised Normal (GNO)

*Generalised Pareto (GPA)

*Gumbel (GUM)

*Kappa (KAP)

*Normal (NOR)

*Pearson III (PE3)

*Wakeby (WAK)

*Weibull (WEI)

The primary function in this file is the samlmu(x,nmom) function, which takes

an input dataset x and input of the number of moments to produce the log

moments of that dataset.

For Instance, given a list "Data", if 5 l-moments are needed, the function

would be called by lmoments.samlmu(Data,5)

In this file contains four different functions for using each distribution.

Each function can be called by the prefix FUN with the suffix DIS.

*PEL: (x,nmom):

Parameter Estimates. This takes the L-Moments calculated by samlmu()

and predicts the parameter estimates for that function.

EXAMPLE: Find Wakeby distribution that best fits dataset DATA:

import lmoments

para = lmoments.pelwak(lmoments.samlmu(DATA,5))

*QUA: (f,para)

Quantile Estimates. This takes the parameter estimates for a

distribution, and a given Quantile value to calculate the quantile for the

given function.

EXAMPLE: Find the Upper Quantile (75%) of the Kappa distribution that

best fits dataset DATA:

import lmoments

para = lmoments.pelkap(lmoments.samlmu(DATA,5))

UQ = lmoments.quakap(0.75,para)

*LMR: (para,nmom):

L-Moment Ratios. This takes the parameter estimates for a distribution

and calculates nmom L-Moment ratios.

EXAMPLE: Find 4 lmoment ratios for the Gumbel distribution that

best fits dataset DATA:

import lmoments

para = lmoments.pelgum(lmoments.samlmu(DATA,5))

LMR = lmoments.lmrgum(para,4)

*CDF: (x,para):

Cumulative Distribution Function. This takes the parameter estimates

for a distribution and calculates the quantile for a given value x.

EXAMPLE: Find the quantile of the datapoint 6.4 for the Weibull

Distribution that best fits the dataset DATA:

import lmoments

para = lmoments.pelwei(lmoments.samlmu(DATA,5))

quantile = lmoments.cdfwei(6.4,para)

*PDF: (x,para):

Probability Distribution Function. This takes the parameter estimates

for a distribution and calculates the p value for a given value x.

EXAMPLE: Find the p-value of the datapoint 6.4 for the Weibull

Distribution that best fits the dataset DATA:

import lmoments

para = lmoments.pelwei(lmoments.samlmu(DATA,5))

quantile = lmoments.pdfwei(6.4,para)

*LMOM: (para):

L-Moment Estimation from Parameters. This function takes the input

parameters for a given distribution, and attempt to calculate the

L-Moments that would correspond to this distribution.

EXAMPLE: Estimate the L-Moments of the Weibull Distribution that has

parameters (2.5,1.5,0.5)

import lmoments

Lmoments = lmoments.lmomwei([2.5,1.5,0.5])

#RAND: (n,para)

Random Number Generator for a given function. This takes a curve fit

and returns a list of random numbers generated from that distribution

EXAMPLE: Generate 10 numbers from the weibull distribution that makes

up the dataset "data"

import lmoments

weibullfit = lmoments.pelwei(lmoments.samlmu(data))

randnums = lmoments.randwei(10,weibullfit)

*NlogL: (data,dist,peldist):

Calculates the Negative Log Likelihood for use in AIC/AICc/BIC calculations.

Provide data, and distribution to calculate NlogL. Can also provide curve

fitting parameters, but if they aren't provided, then the function will

generate them via pelxxx(samlmu(data)). To specify the distribution, use the

three letters typically assigned.

EXAMPLE: Calculate the Negative Log Likelihood of a Gamma distribution

fitted to Data.

import lmoments

NLL = lmoments.NlogL(data,"GAM")

EXAMPLE: Calculate the Negative Log Likelihood of a Gamma distribution

with parameters [2.5,1.0] when fitted to Data.

import lmoments

NLL = lmoments.NlogL(data,"GAM",[2.5,1.0])

*AIC: (data,dist,*distfit):

Calculate the Akaike Information Criterion (AIC) using the chosen dataset

and distribution

EXAMPLE: Calculate the Akaike Information Criterion for the weibull

distribution using the input dataset data:

import lmoments

Akaike = AIC(data,"WEI")

*BIC: (data,dist,*distfit):

Calculate the Bayesian Information Criterion (AIC) using the chosen dataset

and distribution

EXAMPLE: Calculate the Bayesian Information Criterion for the weibull

distribution using the input dataset data:

import lmoments

Akaike = AIC(data,"WEI")

This file contains a Python implimentation of the lmoments.f library created by

J. R. M. HOSKING.

The base Fortran code is copyright of the IBM Corperation, and the licensing

information is shown below:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

IBM software disclaimer

LMOMENTS: Fortran routines for use with the method of L-moments

Permission to use, copy, modify and distribute this software for any purpose

and without fee is hereby granted, provided that this copyright and permission

notice appear on all copies of the software. The name of the IBM Corporation

may not be used in any advertising or publicity pertaining to the use of the

software. IBM makes no warranty or representations about the suitability of the

software for any purpose. It is provided "AS IS" without any express or implied

warranty, including the implied warranties of merchantability, fitness for a

particular purpose and non-infringement. IBM shall not be liable for any direct,

indirect, _special or consequential damages resulting from the loss of use,

data or projects, whether in an action of contract or tort, arising out of or

in connection with the use or performance of this software.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Additional code from the R library "lmomco" has been converted into Python.

This library was developed by WILLIAM ASQUITH, and was released under the GPL-3

License. Copyright (C) 2012 WILLIAM ASQUITH

The Python translation was conducted by:

Sam Gillespie

Numerical Analyst

C&R Consulting

Townsville Australia

September 2013

For more information, or to report bugs, contact:

sam.gillespie@my.jcu.edu.au

Licensing for Python Translation:

####################################################

Copyright (C) 2014 Sam Gillespie

This program 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 should have received a copy of the GNU General Public License

along with this program. If not, see <http://www.gnu.org/licenses/>.Version 0.1.0:

####################################################

Initial Release

Version 0.1.1:

Corrected Small Errors and Typos

Version 0.2.0:

Added Probability Density Functions (PDF)

Added Reverse Lmoment Estimation Functions (LMOM)

Added Negative Log Likelhood Function (NlogL)

Included Unit Tests

Implimented better version of PELWAK function

Support for lists as x inputs for all CDF functions

Bugfixes

Now licensed under the GPLv3

VERSION 0.2.1:

Support for lists as F inputs for all QUA functions

Added Random Number Generator (rand) for all functions

Split the main lmoments.py file into several files, as the

project is getting to large to maintain as one single file.

VERSION 0.2.2:

Improved samlmu function to support any value of nmom

Added Bayesian Information Criterion (BIC) function

Fixed import glitch that allowed users to import container files

General Bugfixes

VERSION 0.2.3

A bug was found that negative floats would be incorrectly handled in some cases.

"""

This library was designed to use L-moments to predict optimal parameters

for a number of distributions. Distributions supported in this file are

listed below, with their distribution suffix:

*Exponential (EXP)

*Gamma (GAM)

*Generalised Extreme Value (GEV)

*Generalised Logistic (GLO)

*Generalised Normal (GNO)

*Generalised Pareto (GPA)

*Gumbel (GUM)

*Kappa (KAP)

*Normal (NOR)

*Pearson III (PE3)

*Wakeby (WAK)

*Weibull (WEI)

The primary function in this file is the samlmu(x,nmom) function, which takes

an input dataset x and input of the number of moments to produce the log

moments of that dataset.

For Instance, given a list "Data", if 5 l-moments are needed, the function

would be called by lmoments.samlmu(Data,5)

In this file contains four different functions for using each distribution.

Each function can be called by the prefix FUN with the suffix DIS.

*PEL: (x,nmom):

Parameter Estimates. This takes the L-Moments calculated by samlmu()

and predicts the parameter estimates for that function.

EXAMPLE: Find Wakeby distribution that best fits dataset DATA:

import lmoments

para = lmoments.pelwak(lmoments.samlmu(DATA,5))

*QUA: (f,para)

Quantile Estimates. This takes the parameter estimates for a

distribution, and a given Quantile value to calculate the quantile for the

given function.

EXAMPLE: Find the Upper Quantile (75%) of the Kappa distribution that

best fits dataset DATA:

import lmoments

para = lmoments.pelkap(lmoments.samlmu(DATA,5))

UQ = lmoments.quakap(0.75,para)

*LMR: (para,nmom):

L-Moment Ratios. This takes the parameter estimates for a distribution

and calculates nmom L-Moment ratios.

EXAMPLE: Find 4 lmoment ratios for the Gumbel distribution that

best fits dataset DATA:

import lmoments

para = lmoments.pelgum(lmoments.samlmu(DATA,5))

LMR = lmoments.lmrgum(para,4)

*CDF: (x,para):

Cumulative Distribution Function. This takes the parameter estimates

for a distribution and calculates the quantile for a given value x.

EXAMPLE: Find the quantile of the datapoint 6.4 for the Weibull

Distribution that best fits the dataset DATA:

import lmoments

para = lmoments.pelwei(lmoments.samlmu(DATA,5))

quantile = lmoments.cdfwei(6.4,para)

*PDF: (x,para):

Probability Distribution Function. This takes the parameter estimates

for a distribution and calculates the p value for a given value x.

EXAMPLE: Find the p-value of the datapoint 6.4 for the Weibull

Distribution that best fits the dataset DATA:

import lmoments

para = lmoments.pelwei(lmoments.samlmu(DATA,5))

quantile = lmoments.pdfwei(6.4,para)

*LMOM: (para):

L-Moment Estimation from Parameters. This function takes the input

parameters for a given distribution, and attempt to calculate the

L-Moments that would correspond to this distribution.

EXAMPLE: Estimate the L-Moments of the Weibull Distribution that has

parameters (2.5,1.5,0.5)

import lmoments

Lmoments = lmoments.lmomwei([2.5,1.5,0.5])

#RAND: (n,para)

Random Number Generator for a given function. This takes a curve fit

and returns a list of random numbers generated from that distribution

EXAMPLE: Generate 10 numbers from the weibull distribution that makes

up the dataset "data"

import lmoments

weibullfit = lmoments.pelwei(lmoments.samlmu(data))

randnums = lmoments.randwei(10,weibullfit)

*NlogL: (data,dist,peldist):

Calculates the Negative Log Likelihood for use in AIC/AICc/BIC calculations.

Provide data, and distribution to calculate NlogL. Can also provide curve

fitting parameters, but if they aren't provided, then the function will

generate them via pelxxx(samlmu(data)). To specify the distribution, use the

three letters typically assigned.

EXAMPLE: Calculate the Negative Log Likelihood of a Gamma distribution

fitted to Data.

import lmoments

NLL = lmoments.NlogL(data,"GAM")

EXAMPLE: Calculate the Negative Log Likelihood of a Gamma distribution

with parameters [2.5,1.0] when fitted to Data.

import lmoments

NLL = lmoments.NlogL(data,"GAM",[2.5,1.0])

*AIC: (data,dist,*distfit):

Calculate the Akaike Information Criterion (AIC) using the chosen dataset

and distribution

EXAMPLE: Calculate the Akaike Information Criterion for the weibull

distribution using the input dataset data:

import lmoments

Akaike = AIC(data,"WEI")

*BIC: (data,dist,*distfit):

Calculate the Bayesian Information Criterion (AIC) using the chosen dataset

and distribution

EXAMPLE: Calculate the Bayesian Information Criterion for the weibull

distribution using the input dataset data:

import lmoments

Akaike = AIC(data,"WEI")

This file contains a Python implimentation of the lmoments.f library created by

J. R. M. HOSKING.

The base Fortran code is copyright of the IBM Corperation, and the licensing

information is shown below:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

IBM software disclaimer

LMOMENTS: Fortran routines for use with the method of L-moments

Permission to use, copy, modify and distribute this software for any purpose

and without fee is hereby granted, provided that this copyright and permission

notice appear on all copies of the software. The name of the IBM Corporation

may not be used in any advertising or publicity pertaining to the use of the

software. IBM makes no warranty or representations about the suitability of the

software for any purpose. It is provided "AS IS" without any express or implied

warranty, including the implied warranties of merchantability, fitness for a

particular purpose and non-infringement. IBM shall not be liable for any direct,

indirect, _special or consequential damages resulting from the loss of use,

data or projects, whether in an action of contract or tort, arising out of or

in connection with the use or performance of this software.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Additional code from the R library "lmomco" has been converted into Python.

This library was developed by WILLIAM ASQUITH, and was released under the GPL-3

License. Copyright (C) 2012 WILLIAM ASQUITH

The Python translation was conducted by:

Sam Gillespie

Numerical Analyst

C&R Consulting

Townsville Australia

September 2013

For more information, or to report bugs, contact:

sam.gillespie@my.jcu.edu.au

Licensing for Python Translation:

####################################################

Copyright (C) 2014 Sam Gillespie

This program 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 should have received a copy of the GNU General Public License

along with this program. If not, see <http://www.gnu.org/licenses/>.Version 0.1.0:

####################################################

Initial Release

Version 0.1.1:

Corrected Small Errors and Typos

Version 0.2.0:

Added Probability Density Functions (PDF)

Added Reverse Lmoment Estimation Functions (LMOM)

Added Negative Log Likelhood Function (NlogL)

Included Unit Tests

Implimented better version of PELWAK function

Support for lists as x inputs for all CDF functions

Bugfixes

Now licensed under the GPLv3

VERSION 0.2.1:

Support for lists as F inputs for all QUA functions

Added Random Number Generator (rand) for all functions

Split the main lmoments.py file into several files, as the

project is getting to large to maintain as one single file.

VERSION 0.2.2:

Improved samlmu function to support any value of nmom

Added Bayesian Information Criterion (BIC) function

Fixed import glitch that allowed users to import container files

General Bugfixes

VERSION 0.2.3

A bug was found that negative floats would be incorrectly handled in some cases.

"""