Generalized Lambda distribution implementation: distributions.genlambda

docs/gallery/genlambda.py

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+# pyright: reportUnknownMemberType=false
+from pathlib import Path
+
+import numpy as np
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+
+from lmo.distributions import genlambda
+
+GALLERY_PATH = Path(__file__).resolve().parent
+TEX_LABEL_TEMPLATE = r'$\beta = {},\ \delta = {}$'
+
+X_MIN, X_MAX = -2, 2
+
+if __name__ == '__main__':
+    plt.style.use([
+        'dark_background',
+        'seaborn-v0_8-poster',
+        GALLERY_PATH.parent / 'styles' / 'gallery.mplstyle',
+    ])
+
+    plt.figure(figsize=(16, 9), dpi=240)
+    palette = mpl.color_sequences['Paired']
+
+    b_denom = 2
+    f = 0
+
+    y_max = 0
+    for b_numer, linestyle in zip([1, -1], ['-', '--']):
+        for i, d in enumerate(range(-2, 3)):
+            b = b_numer / b_denom
+            xa, xb = genlambda.support(b, d, f)
+
+            x = np.linspace(max(X_MIN, xa), min(X_MAX, xb), 1000)
+            y = genlambda.pdf(x, b, d, f)
+            y_max = max(y.max(), y_max)
+
+            plt.plot(
+                x,
+                y,
+                linestyle,
+                label=TEX_LABEL_TEMPLATE.format(
+                    f'{b_numer:+d}/{b_denom}',
+                    f'{d:+d}',
+                ).replace('+', r'\quad\;'),  # (\vphantom requires amsmath)
+                alpha=0.8,
+                color=palette[i]
+            )
+
+    plt.legend()
+    plt.ylabel('$f(X)$', rotation=0)
+    plt.xlabel('$X$')
+    plt.xlim(X_MIN, X_MAX)
+    plt.ylim(0, 1.01 * y_max)
+    plt.title(r'PDF of $X \sim \mathrm{GLD}(\beta, \delta, \phi = 0)$')
+    plt.tight_layout()
+    plt.savefig(
+        GALLERY_PATH / 'genlambda.svg',
+        transparent=True,
+        format='svg',
+        bbox_inches='tight'
+    )
+