Master Copula Theory, Visualization, Estimation, Simulation, and Probability Calculations with the copula Package in R
Sub Category
- Data Science
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Objectives
- 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 and their characteristics
- 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
Pre Requisites
- 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.
FAQ
- Q. How long do I have access to the course materials?
- A. You can view and review the lecture materials indefinitely, like an on-demand channel.
- Q. Can I take my courses with me wherever I go?
- A. Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don't have an internet connection, some instructors also let their students download course lectures. That's up to the instructor though, so make sure you get on their good side!
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