{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Kernel Density Estimation\n", "\n", "Kernel density estimation is the process of estimating an unknown probability density function using a *kernel function* $K(u)$. While a histogram counts the number of data points in somewhat arbitrary regions, a kernel density estimate is a function defined as the sum of a kernel function on every data point. The kernel function typically exhibits the following properties:\n", "\n", "1. Symmetry such that $K(u) = K(-u)$.\n", "2. Normalization such that $\\int_{-\\infty}^{\\infty} K(u) \\ du = 1$ .\n", "3. Monotonically decreasing such that $K'(u) < 0$ when $u > 0$.\n", "4. Expected value equal to zero such that $\\mathrm{E}[K] = 0$.\n", "\n", "For more information about kernel density estimation, see for instance [Wikipedia - Kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation).\n", "\n", "A univariate kernel density estimator is implemented in sm.nonparametric.KDEUnivariate.\n", "In this example we will show the following:\n", "\n", "* Basic usage, how to fit the estimator.\n", "* The effect of varying the bandwidth of the kernel using the bw argument.\n", "* The various kernel functions available using the kernel argument." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:22.792438Z", "iopub.status.busy": "2022-11-02T17:11:22.789566Z", "iopub.status.idle": "2022-11-02T17:11:24.198130Z", "shell.execute_reply": "2022-11-02T17:11:24.197404Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from scipy import stats\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from statsmodels.distributions.mixture_rvs import mixture_rvs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A univariate example" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:24.203933Z", "iopub.status.busy": "2022-11-02T17:11:24.202634Z", "iopub.status.idle": "2022-11-02T17:11:24.208570Z", "shell.execute_reply": "2022-11-02T17:11:24.208010Z" } }, "outputs": [], "source": [ "np.random.seed(12345) # Seed the random number generator for reproducible results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create a bimodal distribution: a mixture of two normal distributions with locations at -1 and 1." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:24.213983Z", "iopub.status.busy": "2022-11-02T17:11:24.212413Z", "iopub.status.idle": "2022-11-02T17:11:24.222060Z", "shell.execute_reply": "2022-11-02T17:11:24.221499Z" } }, "outputs": [], "source": [ "# Location, scale and weight for the two distributions\n", "dist1_loc, dist1_scale, weight1 = -1, 0.5, 0.25\n", "dist2_loc, dist2_scale, weight2 = 1, 0.5, 0.75\n", "\n", "# Sample from a mixture of distributions\n", "obs_dist = mixture_rvs(\n", " prob=[weight1, weight2],\n", " size=250,\n", " dist=[stats.norm, stats.norm],\n", " kwargs=(\n", " dict(loc=dist1_loc, scale=dist1_scale),\n", " dict(loc=dist2_loc, scale=dist2_scale),\n", " ),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The simplest non-parametric technique for density estimation is the histogram." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:24.226546Z", "iopub.status.busy": "2022-11-02T17:11:24.225433Z", "iopub.status.idle": "2022-11-02T17:11:24.479687Z", "shell.execute_reply": "2022-11-02T17:11:24.478976Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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