# Blog thought

#### 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 ...

#### 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 ...

#### Conditional Probability & Bayes Rule

Conditional Probabilities [Latexpage] Let us consider a probability measure $P: \mathcal{A} \rightarrow \mathbb{R}$ of a measurable space $(\Omega, \mathcal{A})$. Further, ...

#### Uncertainty and Capacities in Finance

Monotone Set Functions and the Choquet Integral [Latexpage] The quote of the famous statistician George E. P. Box that "all ...

#### 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 ...

#### Binomial- and Poisson-Mixture Model

[latexpage] Introduction The assumption of independent and identically distributed random variables, short i.i.d., my be quite handy since it simplifies ...

#### Poisson Distribution

[latexpage] Poisson distributions are very important not only for counting events during a fixed period of time but also for ...

#### 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 ...

#### 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 ...