Add diagrams for rand_distr

distr/beta.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import beta
+
+
+def save_to(directory: str, extension: str):
+    # Defining the Beta distribution PDF
+    def y(a, b, x):
+        y = beta.pdf(x, a, b)
+        y[y > 4] = np.nan
+        return y
+
+    inputs = [(0.5, 0.5), (5, 1), (1, 3), (2, 2), (2, 5)]
+    # Possible values for the distribution
+    x = np.linspace(0, 1, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of alpha and beta
+    for a, b in inputs:
+        ax.plot(x, y(a, b, x), label=f'α = {a}, β = {b}')
+
+    # Adding title and labels
+    ax.set_title('Beta distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/beta.{extension}")
+    plt.close()

distr/binomial.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import binom
+
+
+def save_to(directory: str, extension: str):
+    inputs = [(10, 0.2), (10, 0.6)]
+    # Possible outcomes for a Binomial distributed variable
+    outcomes = np.arange(0, 11)
+    width = 0.5
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PMF for each value of n and p
+    for i, (n, p) in enumerate(inputs):
+        ax.bar(outcomes + i * width - width / 2, binom.pmf(outcomes, n, p), width=width, label=f'n = {n}, p = {p}')
+
+    # Adding title and labels
+    ax.set_title('Binomial distribution')
+    ax.set_xlabel('k (number of successes)')
+    ax.set_ylabel('Probability')
+    ax.set_xticks(outcomes)  # set the ticks to be the outcome values
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/binomial.{extension}")
+    plt.close()

distr/cauchy.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def save_to(directory: str, extension: str):
+    # Possible values for the distribution
+    x = np.linspace(-7, 7, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    inputs = [(0, 0.5), (0, 1), (0, 2), (-2, 1)]
+
+    # Plotting the PDF for the Cauchy distribution
+    for x0, gamma in inputs:
+        ax.plot(x, 1 / (np.pi * gamma * (1 + ((x - x0) / gamma)**2)), label=f'x₀ = {x0}, γ = {gamma}')
+
+    # Adding title and labels
+    ax.set_title('Cauchy distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('P(x)')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/cauchy.{extension}")
+    plt.close()

distr/chi_squared.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import chi2
+
+
+def save_to(directory: str, extension: str):
+    def y(x, df):
+        y = chi2.pdf(x, df)
+        y[y > 1.0] = np.nan
+        return y
+    # Degrees of freedom for the distribution
+    df_values = [1, 2, 3, 5, 9]
+    # Possible values for the distribution
+    x = np.linspace(0, 10, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of the degrees of freedom
+    for df in df_values:
+        ax.plot(x, y(x, df), label=f'k = {df}')
+
+    # Adding title and labels
+    ax.set_title('Chi-squared distribution')
+    ax.set_xlabel('Chi-squared statistic')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/chi_squared.{extension}")
+    plt.close()

distr/dirichlet.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import dirichlet
+
+def save_to(directory: str, extension: str):
+    def plot_dirichlet(alpha, ax):
+        """
+        Plots a Dirichlet distribution given alpha parameters and axis.
+        """
+        # Create a 2D meshgrid of points
+        resolution = 200  # Resolution of the visualization
+        x = np.linspace(0, 1, resolution)
+        y = np.linspace(0, 1, resolution)
+        X, Y = np.meshgrid(x, y)
+
+        # Calculate remaining coordinate for the 3-simplex (3D Dirichlet is defined on a triangle in 2D)
+        Z = 1 - X - Y
+
+        # Filter out points outside the triangle
+        valid = Z >= 0
+
+        # Prepare coordinates and the probability density function (PDF) array
+        X = X[valid]
+        Y = Y[valid]
+        Z = Z[valid]
+        points = np.vstack((X, Y, Z)).T  # Stack the valid points
+
+        # Calculate the Dirichlet PDF for valid points
+        PDF = dirichlet.pdf(points, alpha)
+
+        # Reshape PDF back into a 2D array for contour plotting
+        # Initialize full grid PDF to zero (areas outside the triangle remain zero)
+        full_PDF = np.zeros((resolution, resolution))
+        full_PDF[valid] = PDF  # Place the calculated PDF in the valid grid positions
+
+        # Create a contour plot on the provided axis
+        contour = ax.contourf(np.linspace(0, 1, resolution), np.linspace(0, 1, resolution), full_PDF, levels=50, cmap='Blues')
+        plt.colorbar(contour, ax=ax, pad=0.05, aspect=10)
+        ax.set_xlim(0, 1)
+        ax.set_ylim(0, 1)
+        ax.set_xticks([])
+        ax.set_yticks([])
+        ax.set_xlabel(r'$x_1$', fontsize=12)
+        ax.set_ylabel(r'$x_2$', fontsize=12)
+        ax.set_title(r'$\alpha = {}$'.format(alpha), fontsize=14)
+
+    # Define alpha parameters for the Dirichlet distributions to be plotted
+    alpha_params = [
+        (1.5, 1.5, 1.5),
+        (5.0, 5.0, 5.0),
+        (1.0, 2.0, 2.0),
+        (2.0, 4.0, 8.0)
+    ]
+
+    # Create a figure with subplots
+    fig, axes = plt.subplots(2, 2, figsize=(10, 8))
+
+    # Loop through the list of alpha parameters
+    for alpha, ax in zip(alpha_params, axes.flatten()):
+        plot_dirichlet(alpha, ax)
+
+    plt.savefig(f"{directory}/dirichlet.{extension}")
+    plt.close()

distr/exponential.py

@@ -0,0 +1,28 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import expon
+
+
+def save_to(directory: str, extension: str):
+    # Possible values of lambda for the distribution
+    lambda_values = [1, 0.5, 2]
+    # Possible values for the distribution
+    x = np.linspace(0, 5, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of lambda
+    for lmbda in lambda_values:
+        ax.plot(x, expon.pdf(x, scale=1 / lmbda), label=f'λ = {lmbda}')
+
+    # Adding title and labels
+    ax.set_title('Exponential distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/exponential.{extension}")
+    plt.close()

distr/exponential_exp1.py

@@ -0,0 +1,27 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import expon
+
+
+def save_to(directory: str, extension: str):
+    # Fixed value for lambda
+    lmbda = 1
+    # Possible values for the distribution
+    x = np.linspace(0, 5, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of lambda
+    ax.plot(x, expon.pdf(x, scale=1 / lmbda), label=f'λ = {lmbda}')
+
+    # Adding title and labels
+    ax.set_title('Exponential distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/exponential_exp1.{extension}")
+    plt.close()

distr/fisher_f.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import f
+
+
+def save_to(directory: str, extension: str):
+    def y(x, dfn, dfd):
+        y = f.pdf(x, dfn, dfd)
+        y[y > 2.1] = np.nan
+        return y
+
+    # Degrees of freedom for the distribution
+    d1_d2 = [(1, 1), (2, 1), (5, 2), (10, 1), (100, 100)]
+    # Possible values for the distribution
+    x = np.linspace(0, 5, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of the degrees of freedom
+    for m, n in d1_d2:
+        ax.plot(x, y(x, m, n), label=f'm = {m}, n = {n}')
+
+    # Adding title and labels
+    ax.set_title('F-distribution')
+    ax.set_xlabel('F statistic')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/fisher_f.{extension}")
+    plt.close()

distr/frechet.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def save_to(directory: str, extension: str):
+    pass

distr/gamma.py

@@ -0,0 +1,27 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import gamma
+
+
+def save_to(directory: str, extension: str):
+    inputs = [(1, 1), (2, 1), (3, 1), (1, 2), (2, 2), (3, 2)]
+    # Possible values for the distribution
+    x = np.linspace(0, 7, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of alpha and beta
+    for k, theta in inputs:
+        ax.plot(x, gamma.pdf(x, k, scale=theta), label=f'k = {k}, θ = {theta}')
+
+    # Adding title and labels
+    ax.set_title('Gamma distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/gamma.{extension}")
+    plt.close()

distr/geometric.py

@@ -0,0 +1,30 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import geom
+
+
+def save_to(directory: str, extension: str):
+    # Possible values of p for the distribution
+    p_values = [0.2, 0.5, 0.8]
+    # Possible outcomes for a Geometric distributed variable
+    outcomes = np.arange(1, 11)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+    width = 0.2
+
+    # Plotting the PMF for each value of p
+    for i, p in enumerate(p_values):
+        ax.bar(outcomes + i * width - width / 2, geom.pmf(outcomes, p), width=width, label=f'p = {p}')
+
+    # Adding title and labels
+    ax.set_title('Geometric distribution')
+    ax.set_xlabel('Number of trials until first success')
+    ax.set_ylabel('Probability')
+    ax.set_xticks(outcomes)  # set the ticks to be the outcome values
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/geometric.{extension}")
+    plt.close()

distr/gumbel.py

@@ -0,0 +1,27 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import gumbel_r
+
+
+def save_to(directory: str, extension: str):
+    inputs = [(0, 0.5), (0, 1), (0, 2), (-2, 1)]
+    # Possible values for the distribution
+    x = np.linspace(-5, 5, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of mu and beta
+    for mu, beta in inputs:
+        ax.plot(x, gumbel_r.pdf(x, loc=mu, scale=beta), label=f'μ = {mu}, β = {beta}')
+
+    # Adding title and labels
+    ax.set_title('Gumbel distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{directory}/gumbel.{extension}")
+    plt.close()