From 1f5b10868ac1be12444f996e5c26872d6c86f27e Mon Sep 17 00:00:00 2001
From: Daniel van der Hoorn <d.j.vanderhoorn@student.tudelft.nl>
Date: Wed, 8 Jan 2025 19:25:56 +0100
Subject: [PATCH 1/3] Draft report GA 2.7 ready

---
 content/GA_2_7/Report_GA_2_7.md | 77 +++++++++++++++++++++++++++++++++
 1 file changed, 77 insertions(+)
 create mode 100644 content/GA_2_7/Report_GA_2_7.md

diff --git a/content/GA_2_7/Report_GA_2_7.md b/content/GA_2_7/Report_GA_2_7.md
new file mode 100644
index 00000000..c8919604
--- /dev/null
+++ b/content/GA_2_7/Report_GA_2_7.md
@@ -0,0 +1,77 @@
+# Group assignment 2.7 Report: Extreme Value Analysis
+
+*[CEGM1000 MUDE](http://mude.citg.tudelft.nl/).*
+
+**YOUR GROUP NAME HERE**
+
+
+## Primary Task
+
+**Complete the notebook `NOTEBOOK_NAME.ipynb` and write your answers in this document, as requested in the questions below. Note that only part of the notebook results are required to be included in this report.** Typically a short, one-line answer is sufficient; though a simple 'yes' or 'no' is _not_ sufficient. Please include a short reasoning, justification or argumentation.
+
+_You will be graded on the plots and answers provided in this file. You can delete the instructions and any other unnecessary text prior to submission._
+
+**Are you using ChatGPT or similar tools?** _We don't mind, but please don't ask ChatGPT the questions written here and copy/paste whatever answer it gives you - this isn't fun to read and robs you of an opportunity to learn. Try to ask small simple questions to ChatGPT, then read the response carefully and edit it before using it here. It would also be good to ask one or more of your fellow group members to proof-read it before submitting!_ 
+
+## Report Instructions
+
+Remember to use Markdown features to clearly indicate your answers for each question below. 
+
+**Importing figures into a Markdown file:**
+1. Use relative referencing only, with the git repo (working directory) as the root (this is expressed with a single dot `.`)
+2. Our grading systems are case-sensitive so match the names of folders exactly
+3. Use linux-style path separators: `/` rather than `\`.
+4. Do not include spaces in your file path or image name; if it is unavoidable replace the space with `%20`, for example: `![My image](./my%20image.png)`
+
+Here are some examples:
+- an image located in the working directory `![My image](./imagename.ext)` (where `ext` is any image extension).
+- an image located in a sub-directory called "images": `![My image](./images/imagename.ext)`
+- an image with a space in the file name: `![My image](./images/my%20image.png)`
+
+When using Markdown to include an image, the square brackets is a text tag that is displayed in case the image does not load. Do not include a dot in the square brackets; i.e., do _not_ do this: `![my image.](./image.svg)`.
+
+## Questions
+
+**1. Provide a short description of your data set.**
+
+_Your answer here. Include qualitative and quantitative information; do not duplicate the information from the README, but rather the observations you make in Task 1, and anything you think is relevant for the EVA. Don't include a figure of the time series, since that is requested in a later question_
+
+
+**2. What type of distribution do you need to use in the Block Maxima method? Summarize the parameters of this distribution including the tail type. When looking at the fit, would you consider the block maxima method to be appropriate?**
+
+_Your answer here. Summarize the distribution parameters in a Markdown table. Include a semi-log plot of exceedance probability that compares the empirical and fitted distribution. Don't include a figure of the time series, since that is requested in a later question._
+
+_Here is a hint for a simple table; feel free to modify._
+
+| Shape | Location | Scale |
+| :---: | :---: | :---: |
+| ? | ? | ? |
+
+
+**3. What type of distribution do you need to use the Peak over Threshold method? Summarize the parameters of this distribution including the tail type. Do you need to add/subtract the threshold when using this method, and if so, at what point in the analysis do you do so? When looking at the fit, would you consider the peak over threshold method to be appropriate?**
+
+_Your answer here. Summarize the distribution parameters in a Markdown table. Include a semi-log plot of exceedance probability that compares the empirical and fitted distribution. Don't include a figure of the time series, since that is requested in a later question._
+
+
+**4. Comment on any differences you see between the distributions from the two EVA Methods (just one or two sentences, using the figures included above). In terms of information used to fit each distribution, what is the main difference between the two methods?**
+
+_Your answer here. Include a figure of the time series that presents sampled block maxima as red dots and POT samples as blue dots, and refer to this in your answer to the second part of the question._
+
+
+**5. Compare return periods of the event of October 2024 produced by the distributions of the two EVA Methods Explain the reason for the differences you observe.**
+
+_Your answer here. To support your explanation, include the return period figure, as well as a Markdown table that summarizes (quantitatively) the return periods._
+
+
+**6. Which return period would you pick forthe event of October 2024? Justify your answer. Comment also on how you can improve the analysis.**
+
+_Your answer here._
+
+## General Comments on the Assignment [optional]
+
+_Use this space to let us know if you encountered any issues completing this assignment (but please keep it short!). For example, if you encountered an error that could not be fixed in your Python code, or perhaps there was a problem submitting something via GitLab. You can also let us know if the instructions were unclear. You can delete this section if you don't use it._
+
+**End of file.**
+
+<span style="font-size: 75%">
+&copy; Copyright 2023 <a rel="MUDE Team" href="https://studiegids.tudelft.nl/a101_displayCourse.do?course_id=65595">MUDE Teaching Team</a>, TU Delft. This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0 License</a>.
-- 
GitLab


From 835aa95443352ddcf86c69975945227b8f685169 Mon Sep 17 00:00:00 2001
From: pmaresnasarre <p.maresnasarre@tudelft.nl>
Date: Thu, 9 Jan 2025 10:22:02 +0100
Subject: [PATCH 2/3] change notation in task 4 Fri 2.7

---
 content/GA_2_7/rain_solution.ipynb | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/content/GA_2_7/rain_solution.ipynb b/content/GA_2_7/rain_solution.ipynb
index 42193210..169f3e4c 100644
--- a/content/GA_2_7/rain_solution.ipynb
+++ b/content/GA_2_7/rain_solution.ipynb
@@ -775,21 +775,21 @@
     "\n",
     "# Solution:\n",
     "#range of RT\n",
-    "RT_range = np.linspace(1, 800, 500)\n",
+    "return_period_range = np.linspace(1, 800, 500)\n",
     "\n",
-    "#YM&GEV\n",
-    "YM_range = stats.genextreme.ppf(1 - 1/RT_range, *params_YM)\n",
+    "#YM&GEV: transform RT to probabilities and to values of precipitation\n",
+    "YM_range = stats.genextreme.ppf(1 - 1/return_period_range, *params_YM)\n",
     "\n",
-    "#POT&GPD\n",
+    "#POT&GPD: transform RT to probabilities and to values of precipitation\n",
     "average_n_excesses = len(peaks)/YM.shape[0]\n",
-    "non_exc_prob_range = 1 - 1/(RT_range*average_n_excesses)\n",
+    "non_exc_prob_range = 1 - 1/(return_period_range*average_n_excesses)\n",
     "POT_range = stats.genpareto.ppf(non_exc_prob_range, *params_POT) + threshold\n",
     "\n",
     "plt.figure(figsize=(10, 6))\n",
-    "plt.plot(YM_range, RT_range, '--r', label = 'YM&GEV', linewidth=5)\n",
+    "plt.plot(YM_range, return_period_range, '--r', label = 'YM&GEV', linewidth=5)\n",
     "plt.step(ecdf(YM['Prec'])[1], 1/(1 - ecdf(YM['Prec'])[0]),\n",
     "         ':r', label = ' ECDF Yearly maxima')\n",
-    "plt.plot(POT_range, RT_range, 'cornflowerblue', label = 'POT&GPD', linewidth=5)\n",
+    "plt.plot(POT_range, return_period_range, 'cornflowerblue', label = 'POT&GPD', linewidth=5)\n",
     "plt.step(ecdf(P.iloc[peaks, 1])[1], 1/((1 - ecdf(P.iloc[peaks, 1])[0])*average_n_excesses),\n",
     "         linestyle=':', color = 'cornflowerblue', label = 'ECDF POT')\n",
     "plt.plot([771, 771],[0, 1000], '-.k', label = 'Event of October 2024')\n",
@@ -836,7 +836,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -854,7 +854,7 @@
     "YM_RT = 1/(1-stats.genextreme.cdf(771, *params_YM))\n",
     "\n",
     "#POT&GPD\n",
-    "non_exc_prob_range = 1 - 1/(RT_range*average_n_excesses)\n",
+    "non_exc_prob_range = 1 - 1/(return_period_range*average_n_excesses)\n",
     "POT_range = stats.genpareto.ppf(non_exc_prob_range, *params_POT) + threshold\n",
     "\n",
     "#POT&GPD\n",
-- 
GitLab


From fdb4de493db96d284fcf134088714c9b4a4ca682 Mon Sep 17 00:00:00 2001
From: pmaresnasarre <p.maresnasarre@tudelft.nl>
Date: Thu, 9 Jan 2025 13:13:32 +0100
Subject: [PATCH 3/3] report and student versions for Fri 2.7

---
 content/GA_2_7/Analysis.ipynb                 | 497 ++++++++++++++++++
 ...solution.ipynb => Analysis_solution.ipynb} |  63 +--
 content/GA_2_7/GEV_fit.png                    | Bin 0 -> 49482 bytes
 content/GA_2_7/GPD_fit.png                    | Bin 0 -> 47999 bytes
 .../GA_2_7/{Report_GA_2_7.md => Report.md}    |  28 +-
 content/GA_2_7/Report_solved.md               |  67 +++
 content/GA_2_7/return_level_plot.png          | Bin 0 -> 58807 bytes
 content/GA_2_7/sampled_maxima.png             | Bin 0 -> 52519 bytes
 8 files changed, 586 insertions(+), 69 deletions(-)
 create mode 100644 content/GA_2_7/Analysis.ipynb
 rename content/GA_2_7/{rain_solution.ipynb => Analysis_solution.ipynb} (98%)
 create mode 100644 content/GA_2_7/GEV_fit.png
 create mode 100644 content/GA_2_7/GPD_fit.png
 rename content/GA_2_7/{Report_GA_2_7.md => Report.md} (58%)
 create mode 100644 content/GA_2_7/Report_solved.md
 create mode 100644 content/GA_2_7/return_level_plot.png
 create mode 100644 content/GA_2_7/sampled_maxima.png

diff --git a/content/GA_2_7/Analysis.ipynb b/content/GA_2_7/Analysis.ipynb
new file mode 100644
index 00000000..966bab6a
--- /dev/null
+++ b/content/GA_2_7/Analysis.ipynb
@@ -0,0 +1,497 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "be4282e1-88b3-4792-a677-ccd1e429ea57",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "# Group Assignment 2.7: Extreme Value Analysis\n",
+    "\n",
+    "<h1 style=\"position: absolute; display: flex; flex-grow: 0; flex-shrink: 0; flex-direction: row-reverse; top: 60px;right: 30px; margin: 0; border: 0\">\n",
+    "    <style>\n",
+    "        .markdown {width:100%; position: relative}\n",
+    "        article { position: relative }\n",
+    "    </style>\n",
+    "    <img src=\"https://gitlab.tudelft.nl/mude/public/-/raw/main/tu-logo/TU_P1_full-color.png\" style=\"width:100px\" />\n",
+    "    <img src=\"https://gitlab.tudelft.nl/mude/public/-/raw/main/mude-logo/MUDE_Logo-small.png\" style=\"width:100px\" />\n",
+    "</h1>\n",
+    "<h2 style=\"height: 10px\">\n",
+    "</h2>\n",
+    "\n",
+    "*[CEGM1000 MUDE](http://mude.citg.tudelft.nl/): Extreme Value Analysis, Week 2.7, Friday, Jan 10, 2024.*"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "78e9e591-ddfd-403c-8538-6a9559ac462b",
+   "metadata": {
+    "id": "1db6fea9-f3ad-44bc-a4c8-7b2b3008e945"
+   },
+   "source": [
+    "In this project, you will work on the uncertainty of precipitation in Turís, close to Valencia (Spain), where the past 29th October an extreme flood occurred. Turís was the location where the highest rainfall was recorded, being also the record of that station with 771mm in a day.\n",
+    "\n",
+    "<img src=\"https://github.com/patmanas/figs/raw/main/flood_Valencia.avif\" style=\"width:400px\" />\n",
+    "\n",
+    "You have cumulative daily observations since 1999. The dataset was retrieved from the Ministry of Agriculture [here](https://servicio.mapa.gob.es/websiar/SeleccionParametrosMap.aspx?dst=1).\n",
+    "\n",
+    "**The goal of this project is:**\n",
+    "1. Perform Extreme Value Analysis using Yearly Maxima and GEV.\n",
+    "2. Perform Extreme Value Analysis using POT and GPD.\n",
+    "3. Compare the results from both methods and define the return period of the event of October 2024.\n",
+    "\n",
+    "_Read the instructions for this project in `README.md` before beginning the analysis._"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4fc6e87d-c66e-43df-a937-e969acc409f8",
+   "metadata": {
+    "id": "4fc6e87d-c66e-43df-a937-e969acc409f8",
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "from scipy import stats \n",
+    "from scipy.signal import find_peaks\n",
+    "\n",
+    "plt.rcParams.update({'font.size': 14})"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "27fd05f1",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## Task 1: Import and Explore Data\n",
+    "\n",
+    "The first step in the analysis is importing and exploring the data set.\n",
+    "\n",
+    "The dataset has two columns: the first one provides the time stamp of the measurements and the last column shows the measured precipitation (mm). We set the first column as a datetime as they are the dates of the measurements."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "66e2b916-eb89-4d5e-a531-6ff0efa26018",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "# Import\n",
+    "P = pd.read_csv('turis.csv', delimiter = ',', parse_dates = True)\n",
+    "P.columns=['Date', 'Prec'] #rename columns\n",
+    "P['Date'] = pd.to_datetime(P['Date'], format='mixed')\n",
+    "P = P.sort_values(by='Date')\n",
+    "P=P.reset_index(drop=True)\n",
+    "\n",
+    "P.head()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To start the data exploration, we can compute some basic statistics."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4dbeaa1a-84d4-43ad-bebe-cad9e7983c56",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "# values for markdown report\n",
+    "print(f\"{P['Prec'].size:d}\",\n",
+    "      f\"{P['Prec'].min():.3f}\",\n",
+    "      f\"{P['Prec'].max():.3f}\",\n",
+    "      f\"{P['Prec'].mean():.3f}\",\n",
+    "      f\"{P['Prec'].std():.3f}\",\n",
+    "      f\"{P['Prec'].isna().sum():d}\",\n",
+    "      f\"{sum(P['Prec']==0):d}\",\n",
+    "      sep=' | ')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can also plot the timeseries. Notice how the event of October 2024 stands out."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "30390de1-a79e-4d82-ab1b-8abafb91c5f8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Solution\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "plt.plot(P['Date'], P['Prec'],'k')\n",
+    "plt.xlabel('Time')\n",
+    "plt.ylabel('Precipitation [mm]')\n",
+    "plt.grid()\n",
+    "plt.title('Time series of precipitation');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d4886ae8",
+   "metadata": {},
+   "source": [
+    "## Task 2: Yearly Maxima & GEV\n",
+    "\n",
+    "Let's start with the first EVA analysis!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6391c5c2-521c-43f6-919a-ef9a1356fb69",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
+    "<p>\n",
+    "<b>Task 2.1:</b>   \n",
+    "Sample the data set by finding the yearly maxima and add the sampled extremes to your time series plot as red dots.\n",
+    "</p>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "da61b661-a22f-4adc-96f3-d6d494aabfc6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "idx_max = #your code here\n",
+    "YM = P.loc[idx_max]\n",
+    "print('The shape of the sampled extremes is:', YM.shape)\n",
+    "\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "plt.plot(P['Date'], P['Prec'],'k')\n",
+    "plt.scatter(YM['Date'], YM['Prec'], 40, 'r')\n",
+    "plt.xlabel('Time')\n",
+    "plt.ylabel('Precipitation [mm]')\n",
+    "plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1a7eafde-e4c4-427d-bd09-725d049a4310",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
+    "<p>\n",
+    "<b>Task 2.2:</b>   Compute the empirical cumulative distribution function of the sampled maxima. Fit the appropriate extreme value distribution function using <code>scipy.stats</code> and assess the fit via an exceedance plot with semi-log scale.\n",
+    "</p>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "08baa050-e5cf-46bf-aeb0-dcc88b32034b",
+   "metadata": {
+    "id": "0491cc69"
+   },
+   "source": [
+    "<div style=\"background-color:#facb8e; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\"> <p><b>Tip:</b> save the parameters of an instance of <code>rv_continuous</code> as a tuple to make it easier to use the methods of the distribution later.\n",
+    "<br><br>For example, define parameters like this:\n",
+    "<br><code>params = ... .fit( ... )</code>\n",
+    "<br>instead of like this:\n",
+    "<br><code>param1, param2, param3 = ... .fit( ... )</code>\n",
+    "<br>(see WS 2.7 solution for examples).\n",
+    "</p></div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3a47f881",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Function for the ECDF\n",
+    "def ecdf(var):\n",
+    "    #your code here\n",
+    "    return [y, x]\n",
+    "\n",
+    "#Fit the parametric distribution to the extreme observations\n",
+    "params_YM = #your code here\n",
+    "print('GEV parameters are: {:.3f}, {:.3f}, {:.3f}'.format(*params_YM))\n",
+    "\n",
+    "#Compare both the empirical and parametric distributions in semilog scale\n",
+    "#your plot here"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7d9d7835-bde2-4522-a331-7ba07194f573",
+   "metadata": {},
+   "source": [
+    "## Task 3: POT and GPD\n",
+    "\n",
+    "Let's go for Peak Over Threshold (POT)---make sure you **read** this section carefully, as there are some important tips for implementing the method correctly!\n",
+    "\n",
+    "As described in the book: _when performing EVA with POT, we model **excesses** over the threshold, not the actual value of the extreme event._ In principle, this can simply be described as follows:\n",
+    "\n",
+    "$$\n",
+    "X = th + E\n",
+    "$$\n",
+    "\n",
+    "where $X$ is the random variable of interest (rain, in this case), $th$ is the threshold and $E$ is the _excess_ (also a random variable). In other words, the distribution-fitting part of our EVA is performed on $E$. However, it is not practical to verify/validate or make inference with our distribution on the random variable $E$ for two key reasons:\n",
+    "1. It is more convenient to think in terms of $X$, and\n",
+    "2. We often need to calibrate the threshold value, which produces countless different sets of sampled extremes, distributions and random variables, $E$, which cannot be compared easily.\n",
+    "\n",
+    "As such, we continue to perform our analysis in terms of $X$, while making sure to address the fact that our POT data and distributions are defined in terms of $E$. In practical terms, this means we need to <em>add and subtract the threshold value at certain points in the analysis.</em>\n",
+    "\n",
+    "Note: the threshold and declustering time evaluation is outside the scope of MUDE."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "66d85d8b-8e5a-49e0-b93f-780a2ca8c5f5",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
+    "<p>\n",
+    "<b>Task 3.1:</b>   \n",
+    "Apply POT on the timeseries using a declustering time of 48 hours and a threshold of 40mm. Plot the sampled extremes on the timeseries as blue dots.\n",
+    "</p>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "144dc09c-74ef-4278-99b4-9448503a7a97",
+   "metadata": {
+    "id": "0491cc69"
+   },
+   "source": [
+    "<div style=\"background-color:#facb8e; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">Hint: you can use the function <code>find_peaks</code> from Scipy, as done in PA15.</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c200a7b5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "threshold = 40\n",
+    "\n",
+    "distance = 2 #days\n",
+    "peaks, _ = #your code here\n",
+    "print('The shape of the sampled extremes is:', peaks.shape)\n",
+    "\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "plt.plot(P['Date'], P['Prec'],'k')\n",
+    "plt.scatter(P.iloc[peaks, 0], P.iloc[peaks, 1], 40, 'cornflowerblue')\n",
+    "plt.xlabel('Time')\n",
+    "plt.ylabel('Precipitation [mm]')\n",
+    "plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f0841e5c",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
+    "<p>\n",
+    "<b>Task 3.2:</b>   Compute the empirical cumulative distribution function of the sampled maxima. Fit the appropriate extreme value distribution function using <code>scipy.stats</code> and assess the fit via an exceedance plot with semi-log scale.\n",
+    "</p>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24c29446-500a-4259-a8d3-511cdc50a72b",
+   "metadata": {
+    "id": "0491cc69"
+   },
+   "source": [
+    "<div style=\"background-color:#facb8e; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">Hint: you need to fit the appropriate distribution with a location parameter of 0 on the excesses. You can force the fitting of a distribution with a given value of the parameters using the keyword argument <code>floc</code>.</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a8225377-2dc0-4629-8f28-c8fd7d6055bc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "params_POT = #your code here\n",
+    "print('GPD parameters are: {:.3f}, {:.3f}, {:.3f}'.format(*params_POT))\n",
+    "\n",
+    "#your plot here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d976adb0-b5d6-4959-ba0e-05f90a170597",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "# Time series plot with both sets of extremes\n",
+    "# For Report_solution.md\n",
+    "\n",
+    "#your plot here"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c3afa672-64a2-4cc0-9763-4e9b5057e24e",
+   "metadata": {},
+   "source": [
+    "## Task 4: Computing Return Levels\n",
+    "\n",
+    "In this section, we are going to use the distributions found in the previous two Tasks to compute the return periods that correspond to the flood of October 2024 and compare the results that both EVA methods provide."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e41a1a60-c143-420e-b404-14c27e911c67",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
+    "<p>\n",
+    "<b>Task 4.1:</b> create the return level plot for both EVA approaches (values of the random variable in the x-axis and return period on the y-axis; the y-axis in log scale). Consider return periods up to at least 800 years. Add also the return level plot generated using the empirical CDF for both sampling approaches. Plot a line to indicate the magnitude of the event of October 2024 (771mm). \n",
+    "</p>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "740c7fa9-1f1b-4fb9-8425-024ea95b606c",
+   "metadata": {
+    "id": "0491cc69"
+   },
+   "source": [
+    "<div style=\"background-color:#facb8e; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\"> <p>Remember you can use tuple unpacking as an argument for methods of <code>scipy.stats.rv_continuous</code>, like this: <code>*params</code> (see WS 2.7 solution for examples).</p></div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3b50e43c-d801-4779-ac0a-8cef194ceac7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# YOUR_CODE_HERE (more than one line!)\n",
+    "\n",
+    "# plt.figure(figsize=(10, 6))\n",
+    "# plt.plot(YM_range, RT_range, 'r', label = 'YM&GEV')\n",
+    "# plt.plot(POT_range, RT_range, 'cornflowerblue', label = 'POT&GPD')\n",
+    "# YOUR_FIGURE_FORMATTING_CODE_HERE (more than one line!)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
+    "<p>\n",
+    "<b>Task 4.2:</b> What would be the return period associated with the event of October 2024? Compare the answer provided by both approaches and reflect on these differences.\n",
+    "</p>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#YM&GEV\n",
+    "YM_RT = #return period obtained with YM\n",
+    "\n",
+    "#POT&GPD\n",
+    "average_n_excesses = #average numbr of excesses per year\n",
+    "POT_prob = #non exceedance probability\n",
+    "RT_POT = #return period obtained with POT\n",
+    "\n",
+    "#Print\n",
+    "print(f'The return period obtained with YM+GEV is {YM_RT:.3f}\\n'\n",
+    "          f'The return period obtained with POT+GPD is {RT_POT:.3f}\\n')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9c17f83d",
+   "metadata": {},
+   "source": [
+    "**End of notebook.**\n",
+    "\n",
+    "<div style=\"margin-top: 50px; padding-top: 20px; border-top: 1px solid #ccc;\">\n",
+    "  <div style=\"display: flex; justify-content: flex-end; gap: 20px; align-items: center;\">\n",
+    "    <a rel=\"MUDE\" href=\"http://mude.citg.tudelft.nl/\">\n",
+    "      <img alt=\"MUDE\" style=\"width:100px; height:auto;\" src=\"https://gitlab.tudelft.nl/mude/public/-/raw/main/mude-logo/MUDE_Logo-small.png\" />\n",
+    "    </a>\n",
+    "    <a rel=\"TU Delft\" href=\"https://www.tudelft.nl/en/ceg\">\n",
+    "      <img alt=\"TU Delft\" style=\"width:100px; height:auto;\" src=\"https://gitlab.tudelft.nl/mude/public/-/raw/main/tu-logo/TU_P1_full-color.png\" />\n",
+    "    </a>\n",
+    "    <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">\n",
+    "      <img alt=\"Creative Commons License\" style=\"width:88px; height:auto;\" src=\"https://i.creativecommons.org/l/by/4.0/88x31.png\" />\n",
+    "    </a>\n",
+    "  </div>\n",
+    "  <div style=\"font-size: 75%; margin-top: 10px; text-align: right;\">\n",
+    "    &copy; Copyright 2024 <a rel=\"MUDE\" href=\"http://mude.citg.tudelft.nl/\">MUDE</a> TU Delft. \n",
+    "    This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">CC BY 4.0 License</a>.\n",
+    "  </div>\n",
+    "</div>\n",
+    "\n",
+    "\n",
+    "<!--tested with WS_2_8_solution.ipynb-->"
+   ]
+  }
+ ],
+ "metadata": {
+  "colab": {
+   "collapsed_sections": [],
+   "provenance": []
+  },
+  "kernelspec": {
+   "display_name": "multi_more",
+   "language": "python",
+   "name": "multi_more"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.5"
+  },
+  "widgets": {
+   "application/vnd.jupyter.widget-state+json": {
+    "state": {},
+    "version_major": 2,
+    "version_minor": 0
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/content/GA_2_7/rain_solution.ipynb b/content/GA_2_7/Analysis_solution.ipynb
similarity index 98%
rename from content/GA_2_7/rain_solution.ipynb
rename to content/GA_2_7/Analysis_solution.ipynb
index 169f3e4c..fe47599c 100644
--- a/content/GA_2_7/rain_solution.ipynb
+++ b/content/GA_2_7/Analysis_solution.ipynb
@@ -30,12 +30,16 @@
     "id": "1db6fea9-f3ad-44bc-a4c8-7b2b3008e945"
    },
    "source": [
-    "In this project, you will work on the uncertainty of precipitation in Turís, close to Valencia (Spain), where the past month of October an extreme flood occurred. Turís was the location where the highest rainfall was recorded, being also the record of that station with 771mm. You have cumulative daily observations since 1999. The dataset was retrieved from the Ministry of Agriculture [here](https://servicio.mapa.gob.es/websiar/SeleccionParametrosMap.aspx?dst=1).\n",
+    "In this project, you will work on the uncertainty of precipitation in Turís, close to Valencia (Spain), where the past 29th October an extreme flood occurred. Turís was the location where the highest rainfall was recorded, being also the record of that station with 771mm in a day.\n",
+    "\n",
+    "<img src=\"https://github.com/patmanas/figs/raw/main/flood_Valencia.avif\" style=\"width:400px\" />\n",
+    "\n",
+    "You have cumulative daily observations since 1999. The dataset was retrieved from the Ministry of Agriculture [here](https://servicio.mapa.gob.es/websiar/SeleccionParametrosMap.aspx?dst=1).\n",
     "\n",
     "**The goal of this project is:**\n",
     "1. Perform Extreme Value Analysis using Yearly Maxima and GEV.\n",
     "2. Perform Extreme Value Analysis using POT and GPD.\n",
-    "3. Compare the results from both methods in terms of return levels.\n",
+    "3. Compare the results from both methods and define the return period of the event of October 2024.\n",
     "\n",
     "_Read the instructions for this project in `README.md` before beginning the analysis._"
    ]
@@ -382,17 +386,6 @@
     "# plt.savefig('./figures_solution/gev_rain.svg');"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"background-color:#FAE99E; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
-    "    <b>Solution:</b>\n",
-    "    Since we are applying Block Maxima to select the extreme observations, we need to fit the Generalized Extreme Value distributinon (GEV). When assessing the goodness of fit, we can see that the performance is specially poor in the tail, where the event of October 2024 totally deviates from the fit. Also, the fitted distribution underestimates the higher observations, not being on the safe side.\n",
-    "</div>\n",
-    "</div>"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 7,
@@ -611,18 +604,6 @@
     "# plt.savefig('./figures_solution/gpd_rain.svg');"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"background-color:#FAE99E; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
-    "    <b>Solution:</b>\n",
-    "    in this task the threshold is subtracted from the data in the argument of the GPD fitting method (thus fitting the distribution to the excesses). In preparing the plot, note the difference between the way the empirical and theoretical CDF are used: the empirical uses the random variable values directly (the DataFrame column at index 1), whereas the GPD \"adds the threshold back in\" for the random variable value, and uses the excess value as the argument for the CDF.\n",
-    "    Regarding the fitting, the event of October 2024 is not well captured by the distribution. However, the rest of the observations seem to be better described by the distribution function. Thus, POT+GPD seem to provide a better fit that YM+GEV. This could be due to the larger sample of extremes that are obtained when using POT.\n",
-    "</div>\n",
-    "</div>"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 10,
@@ -721,7 +702,7 @@
    "source": [
     "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
     "<p>\n",
-    "<b>Task 4.1:</b> create the return level plot for both EVA approaches (values of the random variable in the x-axis and return period on the y-axis; the y-axis in log scale). Consider return periods up to at least 800 years. Add also he return level plot generated using the empirical CDF for both sampling approaches. Plot a line to indicate the magnitude of the event of October 2024 (771mm). \n",
+    "<b>Task 4.1:</b> create the return level plot for both EVA approaches (values of the random variable in the x-axis and return period on the y-axis; the y-axis in log scale). Consider return periods up to at least 800 years. Add also the return level plot generated using the empirical CDF for both sampling approaches. Plot a line to indicate the magnitude of the event of October 2024 (771mm). \n",
     "</p>\n",
     "</div>"
    ]
@@ -823,20 +804,14 @@
    "source": [
     "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
     "<p>\n",
-    "<b>Task 4.2:</b> What would be the return period associated with the event of October 2024? Compare the answer provided by both approaches and reflect on these differences. You may reflect on:\n",
-    "<li>The source of the differences between both methods.\n",
-    "<li>Which method would be the most reliable in this situation.\n",
-    "<li>If possible, how to improve the reliability of the obtained results.\n",
-    "<li>The meaningfulness of the obtained return periods.\n",
-    "<li>Which return period you would assign to the event if you must assign one.\n",
-    "</li>\n",
+    "<b>Task 4.2:</b> What would be the return period associated with the event of October 2024? Compare the answer provided by both approaches and reflect on these differences.\n",
     "</p>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -854,10 +829,6 @@
     "YM_RT = 1/(1-stats.genextreme.cdf(771, *params_YM))\n",
     "\n",
     "#POT&GPD\n",
-    "non_exc_prob_range = 1 - 1/(return_period_range*average_n_excesses)\n",
-    "POT_range = stats.genpareto.ppf(non_exc_prob_range, *params_POT) + threshold\n",
-    "\n",
-    "#POT&GPD\n",
     "average_n_excesses = len(peaks)/YM.shape[0]\n",
     "POT_prob = stats.genpareto.cdf(771 - threshold, *params_POT)\n",
     "RT_POT = 1/((1-POT_prob)*average_n_excesses)\n",
@@ -867,22 +838,6 @@
     "          f'The return period obtained with POT+GPD is {RT_POT:.3f}\\n')"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"background-color:#FAE99E; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
-    "    <b>Solution:</b>\n",
-    "    <li>The differences are mainly caused by the shape of the tail of the fitted distributions. As shown in the previous plot, the ECDFs computed from YM and from POT are similar, so no significant differences are observed in the sampled extremes. However, the tail of the fitted GEV and GPD are pretty different, being the GEV much more conservative.  \n",
-    "    <li>Based on the fitting of the GPD distribution to the observations, POT+GPD should be more realiable in this case, although we have not performed any analysis on the threshold and declustering time. Therefore, we would need to ensure that the selected extremes are independent.\n",
-    "    <li>Some possibilities to improve the reliability of the method is gathering more data and performing a formal anaysis to assess the threshold and declustering time of POT. We could also look at different ways of fitting the distribution; here, we fitted the coefficients by MLE but there are other approaches such as Bayesian Inference (makes use of previous knowledge to inform the fitting process) or L-moments method, between others. We could also consider weighting the observations to give more relevance to the larger ones to improve the fitting on those, although we would sacrifice the fitting in the smaller ones.\n",
-    "    <li>It is not possible to know as a ground truth what is the return period of the event. However, it gives us an idea of how extreme it is in comparison with other extremes that ocurred and helps us relativize the magnitude of the event. Also, the fitted distributions allow us to assign return periods to values of the random variable (precipitation) that have not occurred yet.\n",
-    "    <li>If I were to choose, I'd go for the return period of the distribution that provides a better fitting to the observations, thus the one obtained using POT+GPD.\n",
-    "</li>\n",
-    "</div>\n",
-    "</div>"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "9c17f83d",
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diff --git a/content/GA_2_7/Report_GA_2_7.md b/content/GA_2_7/Report.md
similarity index 58%
rename from content/GA_2_7/Report_GA_2_7.md
rename to content/GA_2_7/Report.md
index c8919604..9ad6b61c 100644
--- a/content/GA_2_7/Report_GA_2_7.md
+++ b/content/GA_2_7/Report.md
@@ -7,7 +7,7 @@
 
 ## Primary Task
 
-**Complete the notebook `NOTEBOOK_NAME.ipynb` and write your answers in this document, as requested in the questions below. Note that only part of the notebook results are required to be included in this report.** Typically a short, one-line answer is sufficient; though a simple 'yes' or 'no' is _not_ sufficient. Please include a short reasoning, justification or argumentation.
+**Complete the notebook `Analysis.ipynb` and write your answers in this document, as requested in the questions below. Note that only part of the notebook results are required to be included in this report.** Typically a short, one-line answer is sufficient; though a simple 'yes' or 'no' is _not_ sufficient. Please include a short reasoning, justification or argumentation.
 
 _You will be graded on the plots and answers provided in this file. You can delete the instructions and any other unnecessary text prior to submission._
 
@@ -37,33 +37,31 @@ When using Markdown to include an image, the square brackets is a text tag that
 _Your answer here. Include qualitative and quantitative information; do not duplicate the information from the README, but rather the observations you make in Task 1, and anything you think is relevant for the EVA. Don't include a figure of the time series, since that is requested in a later question_
 
 
-**2. What type of distribution do you need to use in the Block Maxima method? Summarize the parameters of this distribution including the tail type. When looking at the fit, would you consider the block maxima method to be appropriate?**
+**2. Yearly Maxima. How many extremes do you sample? What distribution do you need to use together with the Block Maxima sampling method? Summarize the parameters of this distribution including the tail type. Comment on the goodness of fit of the distribution.**
 
-_Your answer here. Summarize the distribution parameters in a Markdown table. Include a semi-log plot of exceedance probability that compares the empirical and fitted distribution. Don't include a figure of the time series, since that is requested in a later question._
+_Your answer here. Summarize the distribution parameters. Include a semi-log plot of exceedance probability that compares the empirical and fitted distribution. Don't include a figure of the time series, since that is requested in a later question._
 
-_Here is a hint for a simple table; feel free to modify._
 
-| Shape | Location | Scale |
-| :---: | :---: | :---: |
-| ? | ? | ? |
+**3. Peak Over Threshold. How many extremes do you sample? What distribution do you need to use together with the POT sampling method? Summarize the parameters of this distribution including the tail type. Comment on the goodness of fit of the distribution. Do you need to add/subtract the threshold when using this method, and if so, at what point in the analysis do you do so?**
 
+_Your answer here. Summarize the distribution parameters. Include a semi-log plot of exceedance probability that compares the empirical and fitted distribution. Don't include a figure of the time series, since that is requested in a later question._
 
-**3. What type of distribution do you need to use the Peak over Threshold method? Summarize the parameters of this distribution including the tail type. Do you need to add/subtract the threshold when using this method, and if so, at what point in the analysis do you do so? When looking at the fit, would you consider the peak over threshold method to be appropriate?**
 
-_Your answer here. Summarize the distribution parameters in a Markdown table. Include a semi-log plot of exceedance probability that compares the empirical and fitted distribution. Don't include a figure of the time series, since that is requested in a later question._
+**4. Comparing the methods. Comment on the differences on the sampled extremes. Comment on the differences you see in the goodness of fit of the distributions from the two EVA Methods (just one or two sentences, using the figures included above). In terms of information used to fit each distribution, are there major differences?**
 
+_Your answer here. Include a figure of the time series that presents sampled block maxima as red dots and POT samples as blue dots, and refer to this in your answer to the first part of the question._
 
-**4. Comment on any differences you see between the distributions from the two EVA Methods (just one or two sentences, using the figures included above). In terms of information used to fit each distribution, what is the main difference between the two methods?**
 
-_Your answer here. Include a figure of the time series that presents sampled block maxima as red dots and POT samples as blue dots, and refer to this in your answer to the second part of the question._
-
-
-**5. Compare return periods of the event of October 2024 produced by the distributions of the two EVA Methods Explain the reason for the differences you observe.**
+**5. Compare return periods of the event of October 2024 produced by the distributions of the two EVA Methods. Reflect on the differences between the two methods and how to tackle them.You may reflect on:**
+- **The source of the differences between both methods.**
+- **Which method would be the most reliable in this situation.**
+- **If possible, how to improve the reliability of the obtained results.**
+- **The meaningfulness of the obtained return periods.**
 
 _Your answer here. To support your explanation, include the return period figure, as well as a Markdown table that summarizes (quantitatively) the return periods._
 
 
-**6. Which return period would you pick forthe event of October 2024? Justify your answer. Comment also on how you can improve the analysis.**
+**6. Which return period would you pick for the event of October 2024? Justify your answer.**
 
 _Your answer here._
 
diff --git a/content/GA_2_7/Report_solved.md b/content/GA_2_7/Report_solved.md
new file mode 100644
index 00000000..e24731f7
--- /dev/null
+++ b/content/GA_2_7/Report_solved.md
@@ -0,0 +1,67 @@
+# Group assignment 2.7 Report: Extreme Value Analysis
+
+*[CEGM1000 MUDE](http://mude.citg.tudelft.nl/).*
+
+**MUDE TEAM**
+
+## Questions
+
+**1. Provide a short description of your data set.**
+
+The dataset contains cumulative daily precipitation between 1999 and 2024, with a total of 8382 observations. The daily precipitation is a physical magnitude with a lower bound in 0, as seen in the minimum value of the observations, and a maximum of 771mm corresponding to the event of 29th October 2024. This event clearly stands out when plotting the timeseries. The mean value of the precipitation if 1.3mm, with a standard deviation of 10.6mm. Other events that stand out when plotting the timeseries are around the year 2001 and 2021.
+
+
+**2. Yearly Maxima. How many extremes do you sample? What distribution do you need to use together with the Block Maxima sampling method? Summarize the parameters of this distribution including the tail type. Comment on the goodness of fit of the distribution.**
+
+26 extremes are sampled, since we have data from 26 years. A Generalized Extreme Value distribution is fitted to the values of the random variable obtaining $\xi=0.426$ (note the change in the symbol), $\mu=45.317$ and $\sigma=29.848$. 
+
+![Goodness of fit of GEV](./GEV_fit.png)
+
+Regarding the goodness of fit, it can be seen in the figure above that the distribution overestimates the exceedance probabilities of the observations between approximately 50mm and 125mm and underestimates them for the observations above approximately 125mm. Moreover, the event of October 2024 is totally out of the fitted distribution. Thus, the fitting of the distribution is not satisfactory.
+
+**3. Peak Over Threshold. How many extremes do you sample? What distribution do you need to use together with the POT sampling method? Summarize the parameters of this distribution including the tail type. Comment on the goodness of fit of the distribution. Do you need to add/subtract the threshold when using this method, and if so, at what point in the analysis do you do so?**
+
+38 extremes are sampled whose excesses follow a Generalized Pareto distribution (GPD). When fitting the GPD using MLE, we obtain $\xi=0.714$ and $\sigma = 14.027$. The location $\mu=0$ since we are fitting to the excesses so we should force it in the fitting.
+
+![Goodness of fit of GPD](./GPD_fit.png)
+
+With regard to the goodness of fit, the distribution seems to fit well the observations until values of the random variable up to 300mm. However, the events above, which is only the one from the event of October 2024, is not well fitted and it is totally out of the tail of the fitted distribution.
+
+The threshold is subtracted from the data in the argument of the GPD fitting method (thus fitting the distribution to the excesses). In preparing the plot, note the difference in the 'Analysis_solution.ipynb' between the way the empirical and theoretical CDF are used: the empirical uses the random variable values directly (the DataFrame column at index 1), whereas the GPD "adds the threshold back in" for the random variable value, and uses the excess value as the argument for the CDF.
+
+**4. Comparing the methods. Comment on the differences on the sampled extremes. Comment on the differences you see in the goodness of fit of the distributions from the two EVA Methods (just one or two sentences, using the figures included above). In terms of information used to fit each distribution, are there major differences?**
+
+![Comparing the sampled maxima](./sampled_maxima.png)
+
+In this case, POT samples 38 extremes, while YM samples 26 extremes. As expected, POT extracts more information from the timeseries but the difference is not dramatic. Playing with the threshold and declustering time could allow extracting more maxima from the timeseries. However, the largest maxima seem to be sampled by both methods, indicating that the phenomenon we are studying has a yearly seasonality. We could also see that if we compare the ECDFs computed with both POT and YM observations.
+
+Regarding the goodness of fit, the event of October 2024 is not well captured by the distribution by any of the methods. However, the other observations seem to be better described by POT+GPD. This could be due to the larger sample of extremes that are obtained when using POT or due to the shape of the tail of the GPD distribution.
+
+**5. Compare return periods of the event of October 2024 produced by the distributions of the two EVA Methods. Reflect on the differences between the two methods and how to tackle them.You may reflect on:**
+- **The source of the differences between both methods.**
+- **Which method would be the most reliable in this situation.**
+- **If possible, how to improve the reliability of the obtained results.**
+- **The meaningfulness of the obtained return periods.**
+
+The return period obtained with YM+GEV is 300.2 years. The return period obtained with POT+GPD is 112.5 years.
+
+![Return level plot](./return_level_plot.png)
+
+- The differences are mainly caused by the shape of the tail of the fitted distributions. As shown in the previous plot, the ECDFs computed from YM and from POT are similar, so no significant differences are observed in the sampled extremes. However, the tail of the fitted GEV and GPD are pretty different, being the GEV much more conservative.  
+- Based on the fitting of the GPD distribution to the observations, POT+GPD should be more realiable in this case, although we have not performed any analysis on the threshold and declustering time. Therefore, we would need to ensure that the selected extremes are independent.
+- Some possibilities to improve the reliability of the method is gathering more data and performing a formal anaysis to assess the threshold and declustering time of POT. We could also look at different ways of fitting the distribution; here, we fitted the coefficients by MLE but there are other approaches such as Bayesian Inference (makes use of previous knowledge to inform the fitting process) or L-moments method, between others. We could also consider weighting the observations to give more relevance to the larger ones to improve the fitting on those, although we would sacrifice the fitting in the smaller ones.
+- It is not possible to know as a ground truth what is the return period of the event. However, it gives us an idea of how extreme it is in comparison with other extremes that ocurred and helps us relativize the magnitude of the event. Also, the fitted distributions allow us to assign return periods to values of the random variable (precipitation) that have not occurred yet.
+
+
+**6. Which return period would you pick for the event of October 2024? Justify your answer.**
+
+If I were to choose, I'd go for the return period of the distribution that provides a better fitting to the observations, thus the one obtained using POT+GPD.
+
+## General Comments on the Assignment [optional]
+
+_Use this space to let us know if you encountered any issues completing this assignment (but please keep it short!). For example, if you encountered an error that could not be fixed in your Python code, or perhaps there was a problem submitting something via GitLab. You can also let us know if the instructions were unclear. You can delete this section if you don't use it._
+
+**End of file.**
+
+<span style="font-size: 75%">
+&copy; Copyright 2023 <a rel="MUDE Team" href="https://studiegids.tudelft.nl/a101_displayCourse.do?course_id=65595">MUDE Teaching Team</a>, TU Delft. This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0 License</a>.
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