Hobby statistics Python project that does the following:
- Compute Expected value E[x], Variance Var[x] and Kurtosis Kur[x] of a fat-tailed Pareto distribution
- Calculate Expected value E[x], Variance Var[x] and Kurtosis Kur[x] using Pareto distribution's calculus definitions
- Compare outcomes
Key learning of this project is as follows:
- For alpha values close to 1, extremely large tail values shall be used to compute Pareto E[x] accurately. That is, the Pareto distribution is truly fat-tailed.
For more information on the Pareto distribution and its properties:
- https://en.wikipedia.org/wiki/Pareto_distribution
- https://wiki.socr.umich.edu/index.php/AP_Statistics_Curriculum_2007_Pareto
- https://math.stackexchange.com/questions/2909207/continuous-pareto-distribution-intuition
- http://www.eclecticon.info/index_htm_files/Probability%20&%20Statistics%20-%20Expectation%20Variance%20Skew%20Kurtosis.pdf
- https://arxiv.org/abs/2001.10488
- https://coffeeandjunk.com/mediocristan-extremistan/