Create app.py

app.py

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+# Import necessary libraries
+import streamlit as st
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import norm
+
+# Define the functions from your code
+def Phi(z):
+    return norm.cdf(z)
+
+def phi(z):
+    return norm.pdf(z)
+
+def f_BCNOLLN(y1, y2, mu1, sigma1, alpha1, beta1, mu2, sigma2, alpha2, beta2, lambd):
+    z1 = (y1 - mu1) / sigma1
+    z2 = (y2 - mu2) / sigma2
+    
+    H1_z1 = Phi(z1)**alpha1 + (1 - Phi(z1))**beta1
+    H2_z2 = Phi(z2)**alpha2 + (1 - Phi(z2))**beta2
+    
+    term1 = (Phi(z1)**alpha1 / H1_z1)**(-lambd)
+    term2 = (Phi(z2)**alpha2 / H2_z2)**(-lambd)
+    common_term = (term1 + term2 - 1)**(-(2*lambd + 1)/lambd)
+    
+    factor1 = (phi(z1) * Phi(z1)**(alpha1 - 1) * (1 - Phi(z1))**(beta1 - 1) *
+               (alpha1 + (beta1 - alpha1) * Phi(z1))) / (sigma1 * H1_z1**2)
+    
+    factor2 = (phi(z2) * Phi(z2)**(alpha2 - 1) * (1 - Phi(z2))**(beta2 - 1) *
+               (alpha2 + (beta2 - alpha2) * Phi(z2))) / (sigma2 * H2_z2**2)
+    
+    pdf = (lambd + 1) * common_term * (factor1 * factor2)
+    
+    return pdf
+
+# Streamlit app
+st.title('BCNOLLN Distribution Visualizer')
+
+# Input fields for parameters
+mu1 = st.sidebar.number_input('Mean μ1', value=0.0)
+sigma1 = st.sidebar.number_input('Standard deviation σ1', value=1.0, min_value=0.1)
+alpha1 = st.sidebar.number_input('Alpha1 α1', value=0.2, min_value=0.0, max_value=1.0)
+beta1 = st.sidebar.number_input('Beta1 β1', value=0.2, min_value=0.0, max_value=1.0)
+
+mu2 = st.sidebar.number_input('Mean μ2', value=0.0)
+sigma2 = st.sidebar.number_input('Standard deviation σ2', value=1.0, min_value=0.1)
+alpha2 = st.sidebar.number_input('Alpha2 α2', value=0.9, min_value=0.0, max_value=1.0)
+beta2 = st.sidebar.number_input('Beta2 β2', value=0.3, min_value=0.0, max_value=1.0)
+
+lambd = st.sidebar.number_input('Lambda λ', value=-0.5)
+
+# Generate y1 and y2 values
+y1, y2 = np.meshgrid(np.linspace(-3, 3, 100), np.linspace(-3, 3, 100))
+
+# Calculate PDF values
+pdf_values = f_BCNOLLN(y1, y2, mu1, sigma1, alpha1, beta1, mu2, sigma2, alpha2, beta2, lambd)
+
+# Plotting
+fig, ax = plt.subplots()
+cp = ax.contourf(y1, y2, pdf_values, cmap='viridis')
+fig.colorbar(cp)
+ax.set_title('BCNOLLN PDF Contour Plot')
+ax.set_xlabel('y1')
+ax.set_ylabel('y2')
+
+st.pyplot(fig)