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Fundamentals of Topology

In this brief post, we investigate the topological foundations of analysis and give some of its first applications. We limit ...
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Probability Integral Transform & Quantile Function Theorem

Introduction We present simple illustrations, explanations and proofs for two very important theorems,
  • the probability integral transformation, and,
  • the quantile ...
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Inner Products, Norms and Metrics

Most people do have an intuitive understanding of the real number system: it is the number system that should be ...
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Conditional Probability & Bayes Rule

Conditional Probabilities Let us consider a probability measure $P: \mathcal{A} \rightarrow \mathbb{R}$ of a measurable space $(\Omega, \mathcal{A})$. Further, let ...
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Uncertainty and Capacities in Finance

Monotone Set Functions and the Choquet Integral The quote of the famous statistician George E. P. Box that "all models ...
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Decision Problems, Risk and Uncertainty

In this post, an introduction to decision-making under risk and uncertainty is provided. To this end, basic concepts and components ...
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Binomial- and Poisson-Mixture Model

Introduction The assumption of independent and identically distributed random variables, short i.i.d., my be quite handy since it simplifies several ...
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Poisson Distribution

Poisson distributions are very important not only for counting events during a fixed period of time but also for different ...
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GPU TensorFlow Installation Guide for Windows

Before we actually start the installation process of the GPU-accelerated Python API of TensorFlow on a Windows platform, we shortly ...
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What is an Empirical Copula?

Introduction Copulas are an important concept in statistics and beyond to describe dependency structures of continuous distributions. However, what can ...
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