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.

Who this course is for

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.
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https://www.udemy.com/course/crash-course-copulas-theory-hands-on-project-with-r/