post list
QuantDare
categories
all

Neural Networks

alarije

all

Foreseeing the future: a user’s guide

Jose Leiva

all

Stochastic portfolio theory, revisited!

P. López

all

“Past performance is no guarantee of future results”, but helps a bit

ogonzalez

all

Playing with Prophet on Financial Time Series (Again)

rcobo

all

Interviewing prices: Don’t settle for less

jramos

all

The Simpson Paradox

kalinda

all

Seeing the market through the trees

xristica

all

Shift or Stick? Should we really ‘sell in May’?

jsanchezalmaraz

all

What to expect when you are the SPX

mrivera

all

K-Means in investment solutions: fact or fiction

T. Fuertes

all

Lévy Flights. Foraging in a Finance blog. Part II

mplanaslasa

all

How to… use bootstrapping in Portfolio Management

psanchezcri

all

What is the difference between Artificial Intelligence and Machine Learning?

ogonzalez

all

Playing with Prophet on Financial Time Series

rcobo

all

Prices Transformation Cheat Sheet

fjrodriguez2

all

Dual Momentum Analysis

J. González

all

Random forest: many are better than one

xristica

all

Non-parametric Estimation

T. Fuertes

all

Classification trees in MATLAB

xristica

all

Using Multidimensional Scaling on financial time series

rcobo

all

Applying Genetic Algorithms to define a Trading System

aparra

all

Graph theory: connections in the market

T. Fuertes

all

Lévy flights. Foraging in a finance blog

mplanaslasa

all

Data Cleansing & Data Transformation

psanchezcri

all

Principal Component Analysis

j3

all

Comparing ETF Sector Exposure Using Chord Diagrams

rcobo

all

Learning with kernels: an introductory approach

ogonzalez

all

SVM versus a monkey. Make your bets.

P. López

all

Clustering: “Two’s company, three’s a crowd”

libesa

all

Euro Stoxx Strategy with Machine Learning

fjrodriguez2

all

Visualizing Fixed Income ETFs with T-SNE

j3

all

Hierarchical clustering, using it to invest

T. Fuertes

all

Lasso applied in Portfolio Management

psanchezcri

all

Markov Switching Regimes say… bear or bullish?

mplanaslasa

all

Exploring Extreme Asset Returns

rcobo

all

Playing around with future contracts

J. González

all

“K-Means never fails”, they said…

fjrodriguez2

all

What is the difference between Bagging and Boosting?

xristica

all

BETA: Upside Downside

j3

all

Outliers: Looking For A Needle In A Haystack

T. Fuertes

all

Autoregressive model in S&P 500 and Euro Stoxx 50

psanchezcri

all

“Let’s make a deal”: from TV shows to identifying trends

mplanaslasa

all

Machine Learning: A Brief Breakdown

libesa

all

Approach to Dividend Adjustment Factor Calculation

J. González

all

Are Low-Volatility Stocks Expensive?

jsanchezalmaraz

all

Predict returns using historical patterns

fjrodriguez2

all

Dream team: Combining classifiers

xristica

all

Stock classification with ISOMAP

j3

all

Could the Stochastic Oscillator be a good way to earn money?

T. Fuertes

all

Sir Bayes: all but not naïve!

mplanaslasa

all

Returns clustering with k-Means algorithm

psanchezcri

all

Correlation and Cointegration

j3

all

Momentum premium factor (II): Dual momentum

J. González

all

Dynamic Markowitz Efficient Frontier

plopezcasado

all

Confusion matrix & MCC statistic

mplanaslasa

all

Prices convolution, a practical approach

fuzzyperson

all

‘Sell in May and go away’…

jsanchezalmaraz

all

S&P 500 y Relative Strength Index II

Tech

all

Performance and correlated assets

T. Fuertes

all

Reproducing the S&P500 by clustering

fuzzyperson

all

Retrocesos y Extensiones de Fibonacci

fjrodriguez2

all

Size Effect Anomaly

T. Fuertes

all

Predicting Gold using Currencies

libesa

all

La Paradoja de Simpson

kalinda

all

Inverse ETFs versus short selling: a misleading equivalence

J. González

all

Random forest vs Simple tree

xristica

all

S&P 500 y Relative Strength Index

Tech

all

Efecto Herding

alarije

all

Cointegración: Seguimiento sobre cruces cointegrados

T. Fuertes

all

Seasonality systems

J. González

all

Una aproximación Risk Parity

mplanaslasa

all

Números de Fibonacci

fjrodriguez2

all

Using Decomposition to Improve Time Series Prediction

libesa

all

Las cadenas de Markov

j3

all

Clasificando el mercado mediante árboles de decisión

xristica

all

Momentum premium factor sobre S&P 500

J. González

all

Árboles de clasificación en Matlab

xristica

all

Fractales y series financieras II

Tech

all

Redes Neuronales II

alarije

all

El gestor vago o inteligente…

jsanchezalmaraz

all

In less of a Bayes haze…

libesa

all

Teoría de Valores Extremos II

kalinda

all

De Matlab a Octave

fuzzyperson

all

Cointegración

T. Fuertes

all

Cópulas: una alternativa en la medición de riesgos

mplanaslasa

all

¿Por qué usar rendimientos logarítmicos?

jsanchezalmaraz

all

Análisis de Componentes Principales

j3

all

Vecinos cercanos en una serie temporal

xristica

all

Redes Neuronales

alarije

all

Fuzzy Logic

fuzzyperson

all

El filtro de Kalman

mplanaslasa

all

Estimación no paramétrica

T. Fuertes

all

Fractales y series financieras

Tech

all

In a Bayes haze…

libesa

all

Volatility of volatility. A new premium factor?

J. González

all

Caso Práctico: Multidimensional Scaling

rcobo

all

Teoría de Valores Extremos

kalinda

all

Central Limit Theorem: Visual demonstration

kalinda

01/12/2015

1
Central Limit Theorem: Visual demonstration

Everybody knows about the Central Limit Theorem, but have you ever seen a visual demonstration?

The Central Limit Theorem states that, given certain conditions, the mean of a large number of iterates of independent random variables will be approximately normally distributed, regardless of the underlying distribution.

Formally,

Let {X1, … , Xn} be a sequence of independent and identically distributed random variables drawn from distributions of expected values given by µ and finite variances given by σ2, then

 CLTFormula

        has a distribution like that of a standard normal distribution N(0,1) for large values of n.

Formulas are nice (if you can understand them!), but it’s always easier to learn things when given a visual demonstration. So let’s try!

As the theorem states, the underlying distribution is not a problem. Therefore, let’s choose an exponential distribution with labmda equal to two for our example.

We draw one thousand random sample of size two from this exponential distribution, take the mean of each pair of two, and plot the histogram of the results.

In this case, the n of theorem would be two, and as we can observe the distribution doesn’t look like a normal distribution:

n equal 2

If we take samples of size ten (n is now ten) and repeat the previous process, the distribution is a little bit more normal:

n equal ten

And as n gets larger, it’s easy to see how the distributions of the sample mean looks more like a normal distribution.

n equal 100n equal 1000

So that’s it! Here you have a nice, easy way to understand what the Central Limit Theorem says!

If you want a bit more fun understanding this theorem, go and visit this video from The New York Times.

Tweet about this on TwitterShare on LinkedInShare on FacebookShare on Google+Email this to someone

add a comment

[…] Central Limit Theorem: Visual demonstration [Quant Dare] Everybody knows about the Central Limit Theorem, but have you ever seen a visual demonstration? The central limit theorem states that, given certain conditions, the mean of a large number of iterates of independent random variables, will be approximately normally distributed, regardless of the underlying distribution. Formally, Let {X1, , Xn} be a sequence of independent and identically […]

wpDiscuz