The area of *combinatorics*, the art of systematic counting, is dreaded territory for many people, so let us bring some light into the matter: in this post we will explain the difference between *permutations* and *combinations*, with and without *repetitions* (also called *replacements*), will calculate the number of possibilities and present efficient R code to enumerate all of them, so read on…

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# Category: Statistics

Posts about statistics

## Learning R: The Ultimate Introduction (incl. Machine Learning!)

There are a million reasons to learn R (see e.g. Why R for Data Science – and not Python?), but where to start? I present to you the ultimate introduction to bring you up to speed! So read on…

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## Was the Bavarian *Abitur* too hard this time?

Bavaria is known for its famous Oktoberfest… and within Germany also for its presumably difficult *Abitur,* a qualification granted by university-preparatory schools in Germany.

A mandatory part for all students is maths. This year many students protested that the maths part was way too hard, they even started an online petition with more than seventy thousand supporters at this time of writing!

It is not clear yet whether their marks will be adjusted upwards, the ministry of education is investigating the case. As a professor in Bavaria who also teaches statistics I will take the opportunity to share with you an actual question from the original examination with solution, so read on…

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## Backtest Trading Strategies Like a Real Quant

R is one of the best choices when it comes to *quantitative finance*. Here we will show you how to load financial data, plot *charts* and give you a step-by-step template to *backtest trading strategies*. So, read on…

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## The Rich didn’t earn their Wealth, they just got Lucky

Tomorrow, on the *First of May*, many countries celebrate the so called *International Workers’ Day* (or *Labour Day*): time to talk about the *unequal distribution of wealth* again, so read on!

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## Base Rate Fallacy – or why No One is justified to believe that Jesus rose

In this post we are talking about one of the most unintuitive results in statistics: the so called *false positive paradox* which is an example of the so called *base rate fallacy*. It describes a situation where a positive test result of a very sensitive medical test shows that you have the respective disease… yet you are most probably healthy!

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## Separating the Signal from the Noise: Robust Statistics for Pedestrians

One of the problems of navigating an autonomous car through a city is to extract *robust signals* in the face of all the *noise* that is present in the different sensors. Just taking something like an arithmetic mean of all the data points could possibly end in a catastrophe: if a part of a wall looks similar to the street and the algorithm calculates an average trajectory of the two this would end in leaving the road and possibly crashing into pedestrians. So we need some robust algorithm to get rid of the noise. The area of statistics that especially deals with such problems is called *robust statistics* and the methods used therein *robust estimation*.

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## Inverse Statistics – and how to create Gain-Loss Asymmetry plots in R

Asset returns have certain statistical properties, also called *stylized facts*. Important ones are:

**Absence of autocorrelation**: basically the direction of the return of one day doesn’t tell you anything useful about the direction of the next day.**Fat tails**: returns are not normal, i.e. there are many more extreme events than there would be if returns were normal.**Volatility clustering**: basically financial markets exhibit high-volatility and low-volatility regimes.**Leverage effect**: high-volatility regimes tend to coincide with falling prices and vice versa.

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## Learning Data Science: Modelling Basics

Data Science is all about building good models, so let us start by building a very simple model: we want to predict monthly income from age (in a later post we will see that age is indeed a good predictor for income).

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## Why R for Data Science – and *Not* Python!

There are literally hundreds of programming languages out there, e.g. the whole alphabet of one letter programming languages is taken. In the area of data science, there are two big contenders: R and Python. Now, why is this blog about R and not Python?

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