# Import necessary libraries import streamlit as st import numpy as np import matplotlib.pyplot as plt from scipy.stats import norm import plotly.graph_objects as go # Define the functions from your code def Phi(z): return norm.cdf(z) def phi(z): return norm.pdf(z) # Define the BCNOLLN CDF based on the provided formula def F_BCNOLLN(y1, y2, mu1, sigma1, alpha1, beta1, mu2, sigma2, alpha2, beta2, lambd): # Convert y1, y2 to z-scores z1 = (y1 - mu1) / sigma1 z2 = (y2 - mu2) / sigma2 # Compute H functions H1_z1 = Phi(z1)**alpha1 + (1 - Phi(z1))**beta1 H2_z2 = Phi(z2)**alpha2 + (1 - Phi(z2))**beta2 # Compute the BCNOLLN CDF term1 = (Phi(z1)*alpha1 / H1_z1)**(-lambd) term2 = (Phi(z2)*alpha2 / H2_z2)**(-lambd) term = term1 + term2 - 1 cdf = term**(-1/lambd) return cdf 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') # Sidebar title and explanation st.sidebar.title('Parameters') st.sidebar.write('Adjust the parameters below to visualize the BCNOLLN distribution.') # Input fields for parameters with sliders mu1 = st.sidebar.slider('Mean μ1', min_value=-10.0, max_value=10.0, value=0.0, step=0.1) sigma1 = st.sidebar.slider('Standard deviation σ1', min_value=0.1, max_value=10.0, value=1.0, step=0.1) alpha1 = st.sidebar.slider('Alpha1 α1', min_value=0.0, max_value=1.0, value=0.2, step=0.01) beta1 = st.sidebar.slider('Beta1 β1', min_value=0.0, max_value=1.0, value=0.2, step=0.01) mu2 = st.sidebar.slider('Mean μ2', min_value=-10.0, max_value=10.0, value=0.0, step=0.1) sigma2 = st.sidebar.slider('Standard deviation σ2', min_value=0.1, max_value=10.0, value=1.0, step=0.1) alpha2 = st.sidebar.slider('Alpha2 α2', min_value=0.0, max_value=1.0, value=0.9, step=0.01) beta2 = st.sidebar.slider('Beta2 β2', min_value=0.0, max_value=1.0, value=0.3, step=0.01) lambd = st.sidebar.slider('Lambda λ', min_value=-1.0, max_value=1.0, value=-0.5, step=0.01) # Generate y1 and y2 values y1, y2 = np.meshgrid(np.linspace(-10, 10, 100), np.linspace(-10, 10, 100)) # Calculate PDF values pdf_values = f_BCNOLLN(y1, y2, mu1, sigma1, alpha1, beta1, mu2, sigma2, alpha2, beta2, lambd) # Calculate CDF values cdf_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.subheader('Results for PDF Plot') # Create a 3D contour plot with Plotly fig = go.Figure(data=[go.Surface(z=pdf_values, x=y1, y=y2, colorscale='Viridis')]) fig.update_layout(title='BCNOLLN PDF 3D Contour Plot', autosize=True, scene=dict( xaxis_title='y1', yaxis_title='y2', zaxis_title='PDF' )) # Display the plot in Streamlit st.plotly_chart(fig) # Create the contour plot fig, ax = plt.subplots() contours = ax.contour(y1, y2, pdf_values, levels=20) ax.clabel(contours, inline=True, fontsize=8, fmt='%.3f') # Add labels to the contours ax.set_xlabel('y1') ax.set_ylabel('y2') ax.set_title('BCEOLLN PDF Distribution Contour Plot') # Display the plot in Streamlit st.pyplot(fig) # Create a 2D contour plot for PDF using Matplotlib fig_2d, ax = plt.subplots() cp = ax.contourf(y1, y2, pdf_values, cmap='viridis') fig_2d.colorbar(cp) ax.set_title('BCNOLLN PDF 2D Contour Plot') ax.set_xlabel('y1') ax.set_ylabel('y2') # Display the PDF plot in Streamlit using Matplotlib st.pyplot(fig_2d) st.subheader('Results for CDF Plot') # Create a 3D contour plot with Plotly fig = go.Figure(data=[go.Surface(z=cdf_values, x=y1, y=y2, colorscale='Viridis')]) fig.update_layout(title='BCNOLLN CDF 3D Contour Plot', autosize=True, scene=dict( xaxis_title='y1', yaxis_title='y2', zaxis_title='CDF' )) # Display the plot in Streamlit st.plotly_chart(fig) # Create the contour plot fig, ax = plt.subplots() contours = ax.contour(y1, y2, cdf_values, levels=20) ax.clabel(contours, inline=True, fontsize=8, fmt='%.3f') # Add labels to the contours ax.set_xlabel('y1') ax.set_ylabel('y2') ax.set_title('BCEOLLN CDF Distribution Contour Plot') # Display the plot in Streamlit st.pyplot(fig) # Create a 2D contour plot for PDF using Matplotlib fig_2d, ax = plt.subplots() cp = ax.contourf(y1, y2, cdf_values, cmap='viridis') fig_2d.colorbar(cp) ax.set_title('BCNOLLN CDF 2D Contour Plot') ax.set_xlabel('y1') ax.set_ylabel('y2') # Display the PDF plot in Streamlit using Matplotlib st.pyplot(fig_2d) # Create a Plotly figure for the 2D contour plot #fig_2d_plotly = go.Figure(data= # go.Contour( # z=cdf_values, # x=y1, # Corresponds to Y1's axis values # y=y2, # Corresponds to Y2's axis values # colorscale='Viridis', # contours=dict( # coloring ='heatmap', # Use 'heatmap' for a filled contour plot # showlabels = True, # Show labels on contours # labelfont = dict( # Label font properties # size = 12, # color = 'white', # ), # ) # ) #) # Update layout of the figure #fig_2d_plotly.update_layout( # title='BCNOLLN CDF 2D Contour Plot', # xaxis_title='y1', # yaxis_title='y2', # autosize=True, #) # Display the plot in Streamlit #st.plotly_chart(fig_2d_plotly) #st.pyplot(fig)