Central Limit Theorem Simulator

Ramiro J. Caro
June 9th 2015

Presentation Source Code

Go to WebApp

Introduction

The Central Limit Theorem (CLT) is one of the most important and useful principles in probability theory.

It states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution.

Our Application will help us to visualize this principle in an easy and interactive way.

Central Limit Theorem Simulator

This is the CLT Simulator interface: Interface

Parameters

In the left side we select the parameters for the simulation.
First we can choose from 3 source distributions:

  • Normal
  • Poisson
  • Exponential

And also set the characteristics value for each of them.

In the lower corner you define the Sample Size and Number of simulations to be run.

Demonstration

(Plots coded in the slide, check R markdown file here or refresh page.) plot of chunk unnamed-chunk-1

Here you can see a simulation using an Exponential Distribution as base, and three histogram with a fix sample size of 60 where it was performed 10, 100 and 1000 simulations.
It's clear that as the number of simulations increase the mean distribution became more Normal.