Package 'ercv'

Title: Fitting Tails by the Empirical Residual Coefficient of Variation
Description: Provides a methodology simple and trustworthy for the analysis of extreme values and multiple threshold tests for a generalized Pareto distribution, together with an automatic threshold selection algorithm. See del Castillo, J, Daoudi, J and Lockhart, R (2014) <doi:10.1111/sjos.12037>.
Authors: Joan del Castillo, David Moriña Soler and Isabel Serra
Maintainer: Isabel Serra <[email protected]>
License: GPL (>= 2)
Version: 1.0.1
Built: 2025-02-13 03:41:10 UTC
Source: https://github.com/cran/ercv

Help Index

Empirical residual coefficient of variation

Description

Fitting tails by the empirical residual coefficient of variation.

Details

Package: ercv
Type: Package
Version: 1.0.1
Date: 2019-09-19
License: GPL version 2 or newer
LazyLoad: yes

The package provides a methodology simple and trustworthy for the analysis of extreme values. The package contains functions for visualizing, fitting and validating the distribution of tails. Moreover, it also provides multiple threshold tests for a generalized Pareto distribution, together with an automatic threshold selection algorithm.

Author(s)

Joan del Castillo (Universitat Autònoma de Barcelona), David Moriña Soler (Catalan Institute of Oncology (ICO)-IDIBELL) and Isabel Serra (Centre de Recerca Matemàtica)

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, evicv, fitpot, ppot, qpot, tdata, thrselect, Tm

EEMBC AutoBench suite (Benchmark 3)

Description

This data corresponds to 1000 observations sampled from the third benchmark of the well-known suite for real-time systems EEMBC AutoBench suite (Poovey, 2007), including a number of of programs used in automotive embedded systems. It corresponds to the basic integer and floating point (BIFP) algorithm.

Usage

BIFP

Format

A numeric vector.

References

Abella J., Padilla, M.,del Castillo, J. & Cazorla, F. (2017). Measurement-Based Worst-Case Execution Time Estimation Using the Coefficient of Variation". ACM Transactions on Design Automation of Electronic Systems (TODAES), 22(4).

Poovey, J. (2007). Characterization of the EEMBC Benchmark Suite. North Carolina State University.

Bilbao waves data set

Description

This data corresponds to the Bilbao waves data set, firstly analysed by Castillo and Hadi (1997) and in del Castillo and Serra (2015) from the MLE point of view.

Usage

bilbao

Format

A numeric vector.

References

Castillo, E. and Hadi, A. S. (1997). Fitting the Generalized Pareto Distribution to Data. Journal of the American Statistical Association, 92, 1609-1620. del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

Plot of complementary empirical distribution function and the complementary distribution function

Description

Plot of complementary empirical distribution function of a sample and the complementary distribution function from peaks-over-threshold model.

Usage

ccdfplot(data, pars=NA, log="y", from=NA, ci=FALSE, main="Complementary cdf", 
  xlab="data", ylab="ccdf", ...)

Arguments

data

a numeric vector.

pars

a list with the set of parameters of peaks-over-threshold model.

log

a character string which contains x if the x axis is to be logarithmic, y if the y axis is to be logarithmic and xy or yx if both axes are to be logarithmic.

from

the origen of x-axis in the plot.

ci

should confidence bands be plotted. Defaults to FALSE.

main

an overall title for the plot.

xlab

horizontal axis label. Defaults to data.

ylab

vertical axis label. Defaults to ccdf.

...

usual graphic parameters.

Value

Plot of complementary empirical distribution function and the complementary distribution function.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, cvevi, cvplot, evicv, fitpot, ppot, qpot, tdata, thrselect, Tm

Examples

data(iFFT)
ccdfplot(iFFT)

Confidence interval for extreme value index

Description

Confidence interval for extreme value index estimation by Tm method.

Usage

cievi(nextremes, evi=0, conf.level=0.90, m=10, nsim=100)

Arguments

nextremes

the number of upper extremes to be used.

evi

extreme value index. In particular, the shape parammeter of a generalized Pareto distribution.

conf.level

confidence level of the interval.

m

number of thresholds to do multiplicial test.

nsim

number of simulation.

Value

A numerical vector with two elements, containing the limits of the interval.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, evicv, fitpot, ppot, qpot, tdata, thrselect, Tm

Examples

cievi(70, evi=0)

Coefficient of variation for a given extreme value index

Description

The coefficient of variation for a given extreme value index in the generalized Pareto distribution.

Usage

cvevi(evi)

Arguments

evi

extreme value index. In particular, the shape parameter of a generalized Pareto distribution. It has to satisfy evi < 1/2.

Value

A numerical value containing the coefficient of variation for the given extreme value index.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, evicv, fitpot, ppot, qpot, tdata, thrselect, Tm

Examples

cvevi(-1)

Exploratory empirical residual coefficient of variation

Description

Exploratory empirical residual coefficient of variation for extreme value analysis.

Usage

cvplot(data, threshold = NA, nextremes = NA, omit=4, evi=0, main="CVplot", 
       conf.level=0.90, xlab="Excluded sample size", 
       ylab="Coefficient of variation", col="blue", ...)

Arguments

data

a numeric vector.

threshold

a threshold value (either this or nextremes must be given but not both).

nextremes

the number of upper extremes to be used (either this or threshold must be given but not both).

omit

the minimum required number of upper extremes for computing residual statistics.

evi

extreme value index. In particular, the shape parammeter of a generalized Pareto distribution.

main

an overall title for the plot.

conf.level

confidence level of the interval (defaults to 0.90).

xlab

horizontal axis label. Defaults to Excluded sample size.

ylab

vertical axis label. Defaults to Coefficient of variation.

col

plot color. Defaults to blue.

...

Usual graphic parameters.

Value

Plot of the empirical residual CV and confidence intervals.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, evicv, fitpot, ppot, qpot, tdata, thrselect, Tm

Examples

data("moby", package = "poweRlaw")
cvplot(moby, main="MobyDick")

data(iFFT)
cvplot(iFFT, threshold=median(iFFT), main="iFFT")

Euro/Dollar daily exchange rates

Description

This data corresponds to the euro/dollar daily exchange rates between 1999 and 2016, including the financial crisis of 2007-2008, which has been generated from the package quantmod (Ryan, 2016).

Usage

EURUSD

Format

A data frame with 6575 rows and 1 column.

References

Ryan, J. A. (2016). quantmod: Quantitative Financial Modelling Framework. R package version 0.4-7. https://CRAN.R-project.org/package=quantmod

Extreme value index

Description

The extreme value index for a given coefficient of variation in the generalized Pareto distribution.

Usage

evicv(cv)

Arguments

cv

coefficient of variation. It has to satisfy cv > 0.

Value

The extreme value index for a given coefficient of variation in the generalized Pareto distribution as a numerical value.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, fitpot, ppot, qpot, tdata, thrselect, Tm

Examples

evicv(2)

EEMBC AutoBench suite (Benchmark 2)

Description

This data corresponds to 1000 observations sampled from the second benchmark of the well-known suite for real-time systems EEMBC AutoBench suite (Poovey, 2007), including a number of of programs used in automotive embedded systems. It corresponds to the fast fourier transform (FFT) algorithm.

Usage

FFT

Format

A numeric vector.

References

Abella J., Padilla, M.,del Castillo, J. & Cazorla, F. (2017). Measurement-Based Worst-Case Execution Time Estimation Using the Coefficient of Variation". ACM Transactions on Design Automation of Electronic Systems (TODAES), 22(4).

Poovey, J. (2007). Characterization of the EEMBC Benchmark Suite. North Carolina State University.

Fits peaks-over-threshold model of a sample

Description

Fits peaks-over-threshold model of a sample.

Usage

fitpot(data, threshold=NA, nextremes=NA, evi=NA)

Arguments

data

a numeric vector.

threshold

a threshold value (either this or nextremes must be given but not both).

nextremes

the number of upper extremes to be used (either this or threshold must be given but not both).

evi

extreme value index. In particular, the shape parammeter of a generalized Pareto distribution.

Value

A data.frame with the following columns:

  • evi extreme value index. In particular, the shape parammeter of a generalized Pareto distribution.

  • psi the scale parameter of a generalized Pareto distribution.

  • threshold a threshold value where peaks-over-threshold is applied.

  • prob proportion of size of data corresponding to the upper extremes modelled with generalized pareto distribution.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, evicv, ppot, qpot, tdata, thrselect, Tm

Examples

data("nidd.thresh", package = "evir")
fitpot(nidd.thresh)

EEMBC AutoBench suite (Benchmark 1)

Description

This data corresponds to 1000 observations sampled from the first benchmark of the well-known suite for real-time systems EEMBC AutoBench suite (Poovey, 2007), including a number of of programs used in automotive embedded systems. It corresponds to the inverse fast fourier transform (iFFT) algorithm.

Usage

iFFT

Format

A numeric vector.

References

Abella J., Padilla, M.,del Castillo, J. & Cazorla, F. (2017). Measurement-Based Worst-Case Execution Time Estimation Using the Coefficient of Variation". ACM Transactions on Design Automation of Electronic Systems (TODAES), 22(4).

Poovey, J. (2007). Characterization of the EEMBC Benchmark Suite. North Carolina State University.

EEMBC AutoBench suite (Benchmark 4)

Description

This data corresponds to 1000 observations sampled from the fourth benchmark of the well-known suite for real-time systems EEMBC AutoBench suite (Poovey, 2007), including a number of of programs used in automotive embedded systems. It corresponds to the matrix arithmetic (MA) algorithm.

Usage

MA

Format

A numeric vector.

References

Abella J., Padilla, M.,del Castillo, J. & Cazorla, F. (2017). Measurement-Based Worst-Case Execution Time Estimation Using the Coefficient of Variation". ACM Transactions on Design Automation of Electronic Systems (TODAES), 22(4).

Poovey, J. (2007). Characterization of the EEMBC Benchmark Suite. North Carolina State University.

Cumulative distribution function

Description

Cumulative distribution function from the peaks-over-threshold model.

Usage

ppot(q, pars, lower.tail=TRUE, log.p=FALSE)

Arguments

q

vector of quantiles.

pars

a numeric vector with the set of parameters of peaks-over-threshold model. The names of the elements have to be evi, psi, threshold, prob.

lower.tail

logical; if TRUE (default), probabilities are P[X≤x]P[X \leq x] otherwise, P[X>x]P[X > x].

log.p

logical; if TRUE probabilities are given as log(p).

Value

Cumulated probability function as a numerical value.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, evicv, fitpot, qpot, tdata, thrselect, Tm

Examples

ppot(1.9, c(evi=0.1, psi=0.2, threshold=0.3, prob=0.4), lower.tail=FALSE)

x<-runif(10000)
x<-c(x^-1,x)
pars<-fitpot(x,1)
ppot(10,pars$coeff,lower.tail=FALSE) #the true value is 0.5/10

Quantile function

Description

Quantile function from the peaks-over-threshold model.

Usage

qpot(p, pars, lower.tail=TRUE, log.p=FALSE)

Arguments

p

vector of probabilities.

pars

a numeric vector with the set of parameters of peaks-over-threshold model. The names of the elements have to be evi, psi, threshold, prob.

lower.tail

logical; if TRUE (default), probabilities are P[X≤x]P[X \leq x] otherwise, P[X>x]P[X > x].

log.p

logical; if TRUE probabilities are given as log(p).

Value

Quantile function as a numerical value.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, evicv, fitpot, ppot, tdata, thrselect, Tm

Examples

qpot(0.1, c(evi=0.1, psi=0.2, threshold=0.3, prob=0.4), lower.tail=FALSE)

x<-runif(10000)
x<-c(x^-1,x)
pars<-fitpot(x,1)
qpot(0.5/10,pars$coeff,lower.tail=FALSE) #the true value is 10

Transforms a heavy-tailed sampled to non-heavy tailed

Description

Transformation of a sample with assumption of heavy-tail to a sample with non-heavy tail.

Usage

tdata(data, threshold = NA, nextremes = NA, sigma=NA)

Arguments

data

a numeric vector.

threshold

a threshold value (either this or nextremes must be given but not both).

nextremes

the number of upper extremes to be used (either this or threshold must be given but not both).

sigma

the scale parammeter divided by shape parameter in generalized Pareto distribution.

Value

The transformed data as a numerical vector.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, evicv, fitpot, ppot, qpot, thrselect, Tm

Examples

data("danish", package = "evir")
tdata(danish)

Threshold selection algorithm

Description

Threshold selection algorithm.

Usage

thrselect(data, threshold=NA, nextremes=NA, omit=16, evi=NA, m=10, nsim=100, 
          conf.level=0.90, oprint=TRUE)

Arguments

data

a numeric vector.

threshold

a threshold value (either this or nextremes must be given but not both).

nextremes

the number of upper extremes to be used (either this or threshold must be given but not both).

omit

the minimum required number of upper extremes for computing residual statistics.

evi

extreme value index. In particular, the shape parammeter of a generalized Pareto distribution.

m

number of thresholds to do multiplicial test.

nsim

number of simulations.

conf.level

confidence level of the interval.

oprint

logical. If TRUE (default), the single solution is printed. In any case, the full solution is the output of the function.

Value

A list including two data.frame (solution and options). Each of the data.frame contains the following columns:

  • m number of thresholds for testing tail index.

  • nextremes number of thresholds for testing tail index.

  • threshold the threshold value

  • rcv residual coefficient of variation for selected threshold.

  • cvopt optimal coefficient of variation for the tail.

  • evi the corresponding tail index for optimal coefficient of variation if evi parameter is NA.

  • tms the statistic of the tail index test.

  • pvalue p-value associated to tms.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, evicv, fitpot, ppot, qpot, tdata, Tm

Examples

data("nidd.thresh", package = "evir")
thrselect(nidd.thresh, nsim=500)

Multiple threshold test for a GPD

Description

Multiple threshold test for a GPD.

Usage

Tm(data, threshold = NA, nextremes = NA, omit = 16, evi = NA, m = 10, nsim = 100)

Arguments

data

a numeric vector.

threshold

a threshold value (either this or nextremes must be given but not both).

nextremes

the number of upper extremes to be used (either this or threshold must be given but not both).

omit

the minimum required number of upper extremes for computing residual statistics.

evi

extreme value index. In particular, the shape parammeter of a generalized Pareto distribution.

m

number of thresholds to do multiplicial test.

nsim

number of simulations.

Value

A data.frame containing the following columns:

  • nextremes the number of upper extremes to be used.

  • cvopt optimal coefficient of variation for the tail.

  • evi the corresponding tail index for optimal coefficient of variation if evi parameter is NA.

  • tms the statistic of the tail index test.

  • pvalue p-value associated to tms.

Author(s)

Joan del Castillo, David Moriña Soler and Isabel Serra

References

del Castillo, J. and Padilla, M. (2016). Modeling extreme values by the residual coefficient of variation. SORT Statist. Oper. Res. Trans. 40(2), 303-320.

del Castillo, J. and Serra, I. (2015). Likelihood inference for Generalized Pareto Distribution. Computational Statistics and Data Analysis, 83, 116-128.

del Castillo, J., Daoudi, J. and Lockhart, R. (2014). Methods to Distinguish Between Polynomial and Exponential Tails. Scandinavian Journal of Statistics, 41, 382-393.

See Also

ercv-package, cievi, ccdfplot, cvevi, cvplot, evicv, fitpot, ppot, qpot, tdata, thrselect

Examples

data("nidd.thresh",package = "evir")
Tm(nidd.thresh,evi=0, nextremes = 75)