Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 23 views

    Session2 Copula

    Uploaded by

    Tuff Buba
    This document provides an overview of using copulas in R, including: - Fitting copula distributions to data using maximum likelihood estimation. - Plotting copulas in 2D and 3D using functions from the copula and plotly packages. - Fitting specific copula families like Clayton, Gaussian, and Gumbel copulas to data. - Calculating Kendall's tau for copulas and empirical data. - Creating tables from matrices and copula objects using the gt package.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Session2 Copula

    Uploaded by

    Tuff Buba
    23 views12 pages
    This document provides an overview of using copulas in R, including: - Fitting copula distributions to data using maximum likelihood estimation. - Plotting copulas in 2D and 3D using functions from the copula and plotly packages. - Fitting specific copula families like Clayton, Gaussian, and Gumbel copulas to data. - Calculating Kendall's tau for copulas and empirical data. - Creating tables from matrices and copula objects using the gt package.

    Original Description:

    Original Title

    Session2_Copula (2)

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    This document provides an overview of using copulas in R, including: - Fitting copula distributions to data using maximum likelihood estimation. - Plotting copulas in 2D and 3D using functions from the copula and plotly packages. - Fitting specific copula families like Clayton, Gaussian, and Gumbel copulas to data. - Calculating Kendall's tau for copulas and empirical data. - Creating tables from matrices and copula objects using the gt package.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    23 views12 pages

    Session2 Copula

    Uploaded by

    Tuff Buba
    This document provides an overview of using copulas in R, including: - Fitting copula distributions to data using maximum likelihood estimation. - Plotting copulas in 2D and 3D using functions from the copula and plotly packages. - Fitting specific copula families like Clayton, Gaussian, and Gumbel copulas to data. - Calculating Kendall's tau for copulas and empirical data. - Creating tables from matrices and copula objects using the gt package.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 12

    Copulas in R

    Alex Isakson

    March 15, 2022

    alex.isakson@cass.city.ac.uk
    Bayes Business School
    Overview

    • Fitting Data: Revision


    • Copulas: Basics and Plotting
    • Copulas: Fitting
    • Creating Tables

    1
    Fitting Data: Revision
    Fitting Data: Revision

    Fit MLE numerically: MASS

    • fitdistr(X, string) : fit data x with distribution from string: ”beta”,


    ”cauchy”, ”chi-squared”, ”exponential”, ”gamma”, ”geometric”,
    ”log-normal”, ”lognormal”, ”logistic”, ”negative binomial”,
    ”normal”, ”Poisson”, ”t” and ”weibull” are possible.

    2
    Copulas: Basics and Plotting
    Copulas: Basics and Plotting

    We use primarily the package copula

    • claytonCopula(par, d) : Clayton copula with parameter par and


    dimension d
    • normalCopula(par, d) : Gaussian copula with parameter par and
    dimension d
    • tCopula(par, d, df) : Gaussian copula with parameter par, degrees
    of freedom df and dimension d
    • gumbelCopula(par, d) : Gumbel copula with parameter par and
    dimension d
    • mvdc(c, m, par m) : distribution made from copula c and margin
    distributions m with parameters par m. Note: m must be a vector of
    strings and par m must be a list

    For more details, see:


    https://cran.r-project.org/web/packages/copula/copula.pdf
    3
    Copulas: Basics and Plotting

    Copulas and Sklar’s theorem:


    For copula objects:

    • pCopula(x, c) : density of the copula c at points x


    • dCopula(x, c) : cdf of the copula c at points x

    • rCopula(n, c) : random number generator of copula c

    For objects made by mvdc:

    • pMvdc(x, mv) : density of the distribution mv at points x


    • dMvdc(x, mv) : cdf of the distribution mv at points x
    • rMvdc(n, mv) : random number generator of distribution mv

    4
    Copulas: Basics and Plotting

    For 3d plotting we use the package plotly

    • plot ly(x = x, y = y, z = M) : compute plot for (x,y,M). Note: M


    is a matrix.
    • add surface() : show plot

    Note: each option after plot ly have to be accompanied by % > %


    A lot of additional recources can be found here: https://plotly.com/r/

    5
    Copulas: Basics and Plotting

    Fast plotting:

    • persp(c, xCopula) : fast 3d plot for density (dCopula) or cdf


    (pCopula) of copula c
    • contour(c, xCopula) : contourplot for density (dCopula) or cdf
    (pCopula) of copula c
    • contourplot2(c, xCopula, col.regions = col) : contourplot for
    density (dCopula) or cdf (pCopula) of copula c

    Note: these work like plot(). So, options like main, xlab, xlim etc. are
    available.

    6
    Copulas: Fitting

    • fitMvdc(x, mv, start) : fit Mvdc for data x and object mvdc. Note:
    start-parameter must be provided in start as a list.
    • fitCopula(c, x, method = ’ml’) : fit MLE for copula c and data x.

    7
    Copulas: Kendall’s Tau

    • tau(c) : calculate Kendall’s tau for copula c.


    • cor(x1, x2, method = ”kendall”) : calculate empirical Kendall’s tau
    for data x1 and x2.

    8
    Creating Tables

    Simple Table:

    • as.table(m) : transform matrix m into a table.


    • write.table(t, file ) : save table t as file.

    Fancy Table:

    • gt(m) : transform matrix m into a gt table.

    • tab header(title = a, subtitle = b ) : option of adding title and


    subtitle.

    Note: each option after gt have to be accompanied by % > %.


    A lot of additional recources can be found here:
    https://gt.rstudio.com/articles/intro-creating-gt-tables.html

    You might also like