remove thebe-init tag from first visible cell

cd50125f · Robert Lanzafame · 1dfd72ae · cd50125f
Commit cd50125f authored 1 year ago by Robert Lanzafame
--- a/book/cookbook/example_gumbel_dont_execute.ipynb
+++ b/book/cookbook/example_gumbel_dont_execute.ipynb
@@ -48,9 +48,7 @@
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
-    "tags": [
-     "thebe-init"
-    ]
+    "tags": []
   },
   "outputs": [],
   "source": [

 %% Cell type:markdown id: tags:

 # Gumbel Distribution Exercise

 Imagine you are concerned with the concentration of an airborne contaminant, $X$, measured in ppm. A previous benchmark study estimates that there is a 10% and 1% chance, respectively, of exceeding 4 and 10 ppm, respectively. You have been asked by the regulatory agency to estimate the contaminant concentration with 0.1% probability of being exceeded. Prior studies suggest that a Gumbel distribution can be used to model contaminant concentration, given by the CDF:

 $$
 F_X(x) = \exp{\Bigg( -\exp{\Big(-\frac{x-\mu}{\beta}\Big)}\Bigg)}
 $$

 Using the cell blocks below as a guide (and also to check your analysis): Task 1) find the parameters of a Gumbel distribution that matches the information provided above, then, Task 2) use it to estimate the concentration with exceedance probability 0.1%.

 To complete this assignment, you can use `numpy`, `matplotlib` and from the `math` library, `log` and `e` (these are imported for you when you inialize the notebook).

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 %pip install ipywidgets

 import matplotlib.pyplot as plt
 from math import log, e
 import numpy as np
 from example_gumbel import check_example
 ```

 %% Cell type:markdown id: tags:

 **Task 0:** fill in the appropriate fitting points:

-%% Cell type:code id: tags:thebe-init
+%% Cell type:code id: tags:

 ``` python
 x_1 = 4
 p_e_1 = _
 x_2 = 10
 p_e_2 = _
 ```

 %% Cell type:markdown id: tags:

 **Task 1:** derive the distribution parameters:

 %% Cell type:code id: tags:

 ``` python
 def gumbel_2_points(x_1, p_e_1, x_2, p_e_2):
    """Compute Gumbel distribution parameters from two points of the CDF.
        Arguments:
            x_1   (float): point one
            p_e_1 (float): probability of exceedance for point one
            x_2   (float): point two
            p_e_2 (float): probability of exceedance for point two
    """

    # YOUR CODE GOES HERE #
    beta = _
    mu = _
    #######################

    return mu, beta
 ```

 %% Cell type:markdown id: tags:

 The cell below will print your parameter values and show a plot to help confirm you have the right implementation.

 %% Cell type:code id: tags:

 ``` python
 mu, beta = gumbel_2_points(x_1, p_e_1, x_2, p_e_2)

 print(f"Your mu: {mu:0.5f}\nYour beta: {beta:0.5f}")

 gumbel_distribution = lambda x: e**(-e**(-(x - mu)/beta))

 plt.title("Gumbel Distribution, $1-F_X(x)$")
 plt.xlabel("Contaminant Concentration, $X$ [ppm]")
 plt.ylabel("Exceedance Probability [--]")
 plt.grid(color='black', linestyle='-', linewidth=0.3)
 x_axis = np.arange(0, 15, 0.1)
 plt.plot(x_axis, np.vectorize(gumbel_distribution)(x_axis), linewidth=2)
 plt.plot(x_1, p_e_1, 'ro')
 plt.annotate("Point 1", (x_1 + 0.4, p_e_1 + 0.02))
 plt.plot(x_2, p_e_2, 'ro')
 plt.annotate("Point 2", (x_2 + 0.4, p_e_2 + 0.001))
 plt.yscale("log")
 plt.show()
 ```

 %% Cell type:markdown id: tags:

 **Task 2:** write a function to solve for the desired random variable value (it will be tested for you with the Check answer button, along with the distribution parameters).

 %% Cell type:code id: tags:

 ``` python
 def find_x_with_probability_p(p):
    """ Compute point in the gumbel distribution for which the CDF is p
        Use the variables mu and beta defined above!
        Hint: they have been defined globally, so you don't need to
                include them as arguments.
    """
    # YOUR CODE GOES HERE #
    x = _
    #######################

    return x
 ```

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 check_example(globals())
 ```

 %% Output



 %% Cell type:code id: tags:

 ``` python
 ```