[SIMULATION] add simulation file to check issue that existed with respect to...

[SIMULATION] add simulation file to check issue that existed with respect to quantile gap in my last presentation

experiment/meteo_france_SCM_study/visualization/study_visualization/main_study_visualizer.py

@@ -97,7 +97,7 @@ def complete_analysis(only_first_one=False):
 
 if __name__ == '__main__':
     # annual_mean_vizu_compare_durand_study(safran=True, take_mean_value=True, altitude=2400)
-    normal_visualization(temporal_non_stationarity=True)
+    normal_visualization(temporal_non_stationarity=False)
     # max_stable_process_vizu_compare_gaume_study(altitude=1800, nb_days=1)
     # extended_visualization()
     # complete_analysis()

thesis_report/simulation_for_quantile_gap.py

+
+
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from extreme_estimator.extreme_models.utils import r, set_seed_r
+
+
+def convergence_quantile_function(zoom=False):
+
+    # Convergence of the quantile function
+    eps = 1e-3
+    left = 0.9 if zoom else eps
+    p = np.linspace(left, 1-eps, 100)
+
+    # n_list = range(1, 10)
+    n_list = [1, 10, 100]
+    for n in n_list:
+        v = r.qexp(np.power(p, 1/n))
+        plt.plot(p, v, label=n)
+        quantile_perfect_gev = np.array(r.qgev(p, shape=0))
+        quantile_perfect_gev += np.log(n)
+        plt.plot(p, quantile_perfect_gev, label='gev' + str(n))
+    plt.legend()
+    plt.show()
+    # remark: convergence is from above, the block maxima quantiles are above its correspond quantile gev distribtuion
+    # this contradicts the hypothesis the issue I raised in "Simulation to understand quantile gap"
+
+
+def convergence_repartition_function():
+    # Convergence of the repartition function
+    lim = 2
+    x = np.linspace(-lim, lim, 100)
+    plt.plot(x, r.pgev(x, shape=0), label='gev')
+    for n in range(1, 20, 5):
+        v = (np.power(r.pexp(x + np.log(n)), n))
+        plt.plot(x, v, label=n)
+    plt.legend()
+    plt.show()
+
+
+if __name__ == '__main__':
+    set_seed_r(seed=21)
+    convergence_quantile_function(zoom=True)
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