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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**What's new :**\n", "- You now understand the problem with extreme quantiles in classical statistics.\n", "- You now know that there exist an extreme value theorem that looks like CLT that tells us there is 3 types of distributions for the max of any random variable, depending on a shape parameter $\\gamma$ : Gumbel, Fréchet, Weibull.\n", "- To fit such a distribution we need a dataset of maximum, and to estimate $\\gamma$, $a_{n}$ (loc) and $b_{n}$ (scale).\n", "- We can do that with scipy.stats.genextreme very quickly.\n", "- With it we can compute extreme quantiles and extreme value propabilities where we have no data to learn !!!\n", "\n", "**What's not new yet:**\n", "- It's sometimes hard to form a dataset of maximums, there is also a similar alternative with threshold levels instead of maximums, which is easier in general. And the distribution to fit is called a GPD (Generalized Pareto Distribution), that is in scipy.stats.pareto.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Thanks for your attention !** **God bless you!**" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }