Random Variable Generation (RVG)

This project repository contains the implementation and results of simulations for three distributions: Beta(5,1), Student's t-distribution with 2 degrees of freedom, and Gamma(2,2). Each distribution was chosen to demonstrate different methods of random variable generation and their applications in statistical analysis.

Project Overview

1. Inverse CDF Method

Used for the Beta(5,1) distribution

Key Steps:

• Generate a uniform random number u
• Transform u using the inverse CDF $F^{-1}(u) = u^{1/5}$

2. Transformation of Random Variables

Applied to generate samples from a Student's t-distribution by transforming variables from standard normal and chi-squared distributions

Key Steps:

• Generate z from N(0, 1) and vfrom $\chi^2(2)$
• Compute $T = \frac{Z}{\sqrt{V/2}}$

3. Accept-Rejection Method

Implemented to sample from Gamma(2,2) using Gamma(2,1) as a proposal distribution

Key Steps:

• Generate a candidate sample from Gamma(2,1)
• Accept or reject the sample based on the calculated acceptance criterion

Repository Files

• RVG.Rmd: Contains all the code for generating the random variables
• RVG.pdf: Knitted pdf of the rmd file