Tag: probability

• The Gumbel Distribution, Extreme Rainfall, and the Euler–Mascheroni Constant

  

  Nature doesn’t just have averages; it has extremes—the hottest day, the strongest wind, the largest daily rainfall, the highest flood. For extremes, a universal statistical law often appears: the Gumbel distribution. In this post, we meet it through a simple and realistic story about annual maximum rainfall, learn how a basic normalization makes its shape…

  Michael Emmerich

  October 13, 2025

  Computational Science, Mathematical Playground

  ai, Coupon Collector, Euler Mascheroni Constant, Gumbel, Gumbel distribution, machine-learning, mathematics, probability, Probability Theory, python, Statistics, Weather Statistics

• The Tent Map – A Simple Path to Chaos

  

  Michael Emmerich, August 20th 2025 Chaotic time series can emerge from very simple deterministic rules. The tent map is a classical example. It shows how fixed points can be unstable, how orbits diverge, and how randomness-like behavior arises from a piecewise linear rule. The Tent Map The tent map is defined on the interval by…

  Michael Emmerich

  August 19, 2025

  Chaos Theory, Computational Science, Mathematical Playground, Prime Numbers, Small Python Math Examples

  Binary Shift Map, Chaos Theory, Dynamical Systems, mathematics, Periodic Maps, Prime Numbers, probability, Tent Map