Crash Course: Copulas – Theory & Hands-On Project With R
Published 3/2025
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 208.84 MB | Duration: 0h 58m
Published 3/2025
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 208.84 MB | Duration: 0h 58m
Master Copula Theory, Visualization, Estimation, Simulation, and Probability Calculations with the copula Package in R
What you'll learn
Understand the fundamentals of copulas – Learn what copulas are, their mathematical properties, and their role in modeling dependence structures
Explore Sklar’s Theorem – Understand how joint cumulative distribution functions (CDFs) decompose into marginal distributions and a copula function
Learn different types of copulas – Study Gaussian, t-Student, Clayton, and Gumbel copulas, their characteristics, and how they capture different dependence stru
Estimate copula parameters in R – Use the copula package to estimate copula parameters through statistical methods
Perform goodness-of-fit tests – Assess the quality of fitted copula models using statistical criteria such as AIC, BIC, and log-likelihood
Visualize copulas in R – Generate contour plots, 3D surfaces, and scatter plots to interpret dependence structures
Simulate data using copulas – Use copulas to generate synthetic datasets that preserve the dependence structure of modeled data
Analyze dependencies – Compute Kendall’s Tau, Spearman’s Rho, and tail dependence coefficients to measure both typical and extreme event correlations
Requirements
Basic understanding of probability and statistics – Familiarity with concepts such as probability density functions (PDFs), cumulative distribution functions (CDFs), joint, marginal, and conditional distributions, as well as correlation.
Basic knowledge of statistical modeling and data analysis.
Familiarity with mathematical functions and their characteristics.
Willingness to work with mathematical formulas and apply them in R.
Ability to install and use R and RStudio on a computer.
Access to a computer with an internet connection to download necessary packages.
Introductory experience with R programming – Including data import, working with basic functions, and handling variables.
Curiosity and motivation to learn copula theory and its applications.
Patience and persistence to analyze dependencies between variables and apply copula-based techniques.
Description
"Crash Course: Copulas – Theory & Hands-On Project with R” is designed to introduce you to copula theory and its applications in statistical modeling using R. This course provides a structured approach to understanding copulas, from fundamental concepts to hands-on implementation with toy data.Who Is This Course For?No prior knowledge of copulas? No problem! This course is ideal for: Data scientists, statisticians, and analysts looking to model dependencies between variables. Finance, actuarial science, and risk management professionals interested in advanced dependence structures.Researchers and students seeking practical applications of copula models in various fields.R users looking to expand their skills with copula-based statistical modeling.What Does the Course Include?This course provides a comprehensive mix of theory and practice, ensuring a deep understanding of copulas and their real-world applications. You will: Learn the mathematical foundations of copulas, including Sklar’s Theorem. Explore different types of copulas – Gaussian, t-Student, Clayton, and Gumbel. Estimate copula parameters using the copula package in R. Perform goodness-of-fit tests to evaluate copula models. Visualize copula structures using scatter plots, contour plots, and 3D surfaces.Simulate and analyze dependencies using copula-based models. Compute marginal, joint, and conditional probabilities using copulas.Additional Learning ResourcesTo enhance your learning experience, this course includes practical coding exercises and step-by-step R implementations to reinforce key concepts.Why Take This Course?By the end of this course, you will be able to: Model and analyze dependencies between variables using copulas. Use R efficiently to implement copula-based statistical modeling. Apply copula models in finance, risk management, insurance, and data science.Ready to Get Started?Dive into the world of copulas and discover how they can revolutionize dependence modeling in statistics and data science.
Overview
Section 1: Introduction
Lecture 1 Introductory Notes
Section 2: Course Resources
Lecture 2 Course Resources
Section 3: A Brief Guide to Four Fundamental Copulas
Lecture 3 An Introduction to Copulas
Lecture 4 Copulas Adressed: Basic Characteristics
Lecture 5 d-Dimensional Copula Function
Lecture 6 Interactive 3D Plot Demonstrating Basic Properties of a Bivariate Copula
Lecture 7 Sklar's Theorem
Lecture 8 Elliptical Copulas: Multivariate Gaussian Copula
Lecture 9 Elliptical Copulas: Bivariate Gaussian Copula
Lecture 10 Gaussian Copula: Scatter Plots
Lecture 11 Elliptical Copulas: Multivariate t-Student Copula (t-Copula)
Lecture 12 Elliptical Copulas: Bivariate t-Student Copula (t-Copula)
Lecture 13 t-Copula: Scatter Plots
Lecture 14 Archimedean Copulas: Multivariate Clayton Copula
Lecture 15 Archimedean Copulas: Bivariate Clayton Copula
Lecture 16 Clayton Copula: Scatter Plots
Lecture 17 Archimedean Copulas: Multivariate Gumbel Copula
Lecture 18 Archimedean Copulas: Bivariate Gumbel Copula
Lecture 19 Gumbel Copula: Scatter Plots
Lecture 20 Tail Dependence
Lecture 21 Correlation
Lecture 22 Interactive Scatter Plots for Copulas: Gaussian, t, Clayton, and Gumbel
Lecture 23 t-Copula: Spearman’s Rho vs t-Copula Parameter
Lecture 24 Clayton Copula: Spearman’s Rho vs Clayton Copula Parameter
Lecture 25 Gumbel Copula: Spearman’s Rho vs Gumbel Copula Parameter
Section 4: Study of Two-Dimensional Distributions of Random Variable Using R copula package
Lecture 26 Copula R Project
Lecture 27 R packages
Lecture 28 Data Import
Lecture 29 Data Visualization
Lecture 30 Independence Test of Random Variables
Lecture 31 Data Transformation
Lecture 32 Copula Parameter Estimation
Lecture 33 Analysis of Estimated Parameters
Lecture 34 Verification of Fit Quality of Parameters
Lecture 35 Selection of the Best Copula
Lecture 36 Visual Analysis of the Copula
Lecture 37 Analysis of Correlation Dependencies
Lecture 38 Data Simulation
Lecture 39 Probability Calculations
Undergraduate and graduate students in statistics, mathematics, finance, economics, actuarial science, or related fields who want to understand dependence structures using copulas.,Data analysts, statisticians, and researchers interested in modeling and analyzing relationships between random variables beyond traditional correlation methods.,Finance and risk management professionals who need to model financial dependencies, portfolio risks, and credit scoring using copulas.,Actuaries and insurance analysts looking to apply copula models for risk aggregation and loss modeling.,Self-learners and R users eager to expand their knowledge of advanced statistical modeling techniques and hands-on R implementations.