Oluwalkemdown/SamplingDistribution

1import streamlit as st2import numpy as np3import matplotlib.pyplot as plt4 5# -------------------------------6# Page Configuration7# -------------------------------8st.set_page_config(9    page_title="Sampling Distribution Simulator",10    layout="wide"11)12 13st.title("📊 Sampling Distribution Simulator")14st.caption("Explore how the sampling distribution of the mean behaves (CLT in action).")15 16# -------------------------------17# Sidebar Controls18# -------------------------------19st.sidebar.header("Population Settings")20 21distribution = st.sidebar.selectbox(22    "Population Distribution",23    ["Normal", "Uniform", "Exponential", "Bimodal"]24)25 26population_size = st.sidebar.slider(27    "Population Size",28    min_value=1000,29    max_value=100000,30    step=1000,31    value=1000032)33 34st.sidebar.header("Sampling Settings")35 36sample_size = st.sidebar.slider(37    "Sample Size (n)",38    min_value=1,39    max_value=200,40    value=3041)42 43num_samples = st.sidebar.slider(44    "Number of Samples",45    min_value=10,46    max_value=5000,47    step=10,48    value=100049)50 51# -------------------------------52# Generate Population53# -------------------------------54np.random.seed(42)55 56if distribution == "Normal":57    mu = st.sidebar.slider("Mean (μ)", -10.0, 10.0, 0.0)58    sigma = st.sidebar.slider("Std Dev (σ)", 0.5, 10.0, 2.0)59    population = np.random.normal(mu, sigma, population_size)60 61elif distribution == "Uniform":62    low = st.sidebar.slider("Lower Bound", -20.0, 0.0, -5.0)63    high = st.sidebar.slider("Upper Bound", 0.0, 20.0, 5.0)64    population = np.random.uniform(low, high, population_size)65 66elif distribution == "Exponential":67    scale = st.sidebar.slider("Scale (1/λ)", 0.5, 10.0, 2.0)68    population = np.random.exponential(scale, population_size)69 70elif distribution == "Bimodal":71    mu1 = st.sidebar.slider("Mean 1", -10.0, 0.0, -3.0)72    mu2 = st.sidebar.slider("Mean 2", 0.0, 10.0, 3.0)73    sigma = st.sidebar.slider("Std Dev", 0.5, 5.0, 1.5)74    population = np.concatenate([75        np.random.normal(mu1, sigma, population_size // 2),76        np.random.normal(mu2, sigma, population_size // 2)77    ])78 79# -------------------------------80# Sampling81# -------------------------------82sample_means = []83single_sample = np.random.choice(population, size=sample_size, replace=True)84 85for _ in range(num_samples):86    sample = np.random.choice(population, size=sample_size, replace=True)87    sample_means.append(np.mean(sample))88 89sample_means = np.array(sample_means)90 91# -------------------------------92# Layout93# -------------------------------94col1, col2, col3 = st.columns(3)95 96# -------------------------------97# Population Plot98# -------------------------------99with col1:100    st.subheader("Population Distribution")101    fig, ax = plt.subplots()102    ax.hist(population, bins=40, density=True)103    ax.set_xlabel("Value")104    ax.set_ylabel("Density")105    st.pyplot(fig)106 107# -------------------------------108# Single Sample Plot109# -------------------------------110with col2:111    st.subheader("One Random Sample")112    fig, ax = plt.subplots()113    ax.hist(single_sample, bins=20, density=True)114    ax.axvline(np.mean(single_sample), linestyle="--", label="Sample Mean")115    ax.legend()116    ax.set_xlabel("Value")117    st.pyplot(fig)118 119# -------------------------------120# Sampling Distribution Plot121# -------------------------------122with col3:123    st.subheader("Sampling Distribution of the Mean")124    fig, ax = plt.subplots()125    ax.hist(sample_means, bins=40, density=True)126    ax.axvline(np.mean(sample_means), linestyle="--", label="Mean of Sample Means")127    ax.set_xlabel("Sample Mean")128    ax.legend()129    st.pyplot(fig)130 131# -------------------------------132# Statistics Display133# -------------------------------134st.markdown("---")135st.subheader("📈 Summary Statistics")136 137colA, colB, colC = st.columns(3)138 139with colA:140    st.metric("Population Mean", f"{np.mean(population):.3f}")141    st.metric("Population Std Dev", f"{np.std(population):.3f}")142 143with colB:144    st.metric("Sample Mean", f"{np.mean(single_sample):.3f}")145    st.metric("Sample Std Dev", f"{np.std(single_sample):.3f}")146 147with colC:148    st.metric("Mean of Sample Means", f"{np.mean(sample_means):.3f}")149    st.metric("Std Dev of Sample Means", f"{np.std(sample_means):.3f}")150 151st.caption("As sample size increases, the sampling distribution becomes more normal and its spread shrinks (Central Limit Theorem).")152