{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5e1851be",
   "metadata": {},
   "source": [
    "# Univariate Plots\n",
    "\n",
    "Univariate EDA assumes the model **y = c + e** — a fixed location `c` plus\n",
    "random error `e`.  The goal is to characterise the distribution of `e`\n",
    "and check whether the data are truly random and stationary.\n",
    "\n",
    "Reference: [NIST Handbook Chapter 1.3.3](https://www.itl.nist.gov/div898/handbook/eda/section3/eda33.htm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "893271e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from drippy import EDAData\n",
    "from drippy import (\n",
    "    run_sequence_plot,\n",
    "    lag_plot,\n",
    "    histogram,\n",
    "    normal_probability_plot,\n",
    "    four_plot,\n",
    "    ppcc_plot,\n",
    "    weibull_plot,\n",
    "    probability_plot,\n",
    "    box_cox_normality_plot,\n",
    "    bootstrap_plot,\n",
    "    box_cox_linearity_plot,\n",
    ")\n",
    "\n",
    "rng = np.random.default_rng(42)\n",
    "\n",
    "# Normal data — 200 ceramic-strength-like measurements\n",
    "y = rng.normal(loc=688.0, scale=65.0, size=200)\n",
    "data = EDAData(y=y)\n",
    "\n",
    "# Positive-only data — component lifetimes following a Weibull distribution\n",
    "y_pos = rng.weibull(2.0, size=100) * 500\n",
    "data_pos = EDAData(y=y_pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc54e19e",
   "metadata": {},
   "source": [
    "## Run Sequence Plot  (NIST 1.3.3.25)\n",
    "\n",
    "Plots `y` in the order the measurements were taken.  Drifts, shifts, or\n",
    "periodic patterns visible here indicate the data are **not** stationary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8e080d58",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = run_sequence_plot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0743aedc",
   "metadata": {},
   "source": [
    "Supply a physical time axis via `t`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "243283c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.linspace(0, 10, 200)\n",
    "data_t = EDAData(y=y, t=t)\n",
    "fig, ax = run_sequence_plot(data_t)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9150248",
   "metadata": {},
   "source": [
    "## Lag Plot  (NIST 1.3.3.15)\n",
    "\n",
    "Scatters `y[i]` against `y[i − lag]`.  A structureless cloud confirms\n",
    "randomness; patterns (lines, ellipses) reveal autocorrelation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aa18cfe5",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = lag_plot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31f78c2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = lag_plot(data, lag=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ad18d25",
   "metadata": {},
   "source": [
    "## Histogram  (NIST 1.3.3.14)\n",
    "\n",
    "Shows the frequency distribution of `y`.  Look for symmetry, outliers,\n",
    "and whether the shape matches a known family."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "578f3a06",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = histogram(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ece61d4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = histogram(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b27ad559",
   "metadata": {},
   "source": [
    "## Normal Probability Plot  (NIST 1.3.3.21)\n",
    "\n",
    "Ordered data against normal quantiles.  A straight line indicates\n",
    "normality; curvature suggests skew or heavy tails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "506cfd29",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax, _ = normal_probability_plot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "889ed424",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax, rsq = normal_probability_plot(data, return_rsquared=True)\n",
    "print(f\"R² = {rsq:.4f}\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "073fec4a",
   "metadata": {},
   "source": [
    "## 4-Plot  (NIST 1.3.3.5)\n",
    "\n",
    "The 4-plot combines the run-sequence plot, lag plot, histogram, and normal\n",
    "probability plot in a single 2×2 figure — the recommended first step for\n",
    "any univariate EDA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "504e9265",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = four_plot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92a11d98",
   "metadata": {},
   "source": [
    "## PPCC Plot  (NIST 1.3.3.6)\n",
    "\n",
    "The Probability Plot Correlation Coefficient (PPCC) plot finds the shape\n",
    "parameter of a distribution family that best fits the data.  The rough\n",
    "panel locates the maximum; the fine panel zooms in."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "790a2b33",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = ppcc_plot(data_pos)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc29ce09",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = ppcc_plot(data_pos, rough_range=(0.5, 3.0))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e4ac7dd",
   "metadata": {},
   "source": [
    "## Weibull Plot  (NIST 1.3.3.30)\n",
    "\n",
    "Linearised Weibull probability plot for positive failure-time or\n",
    "strength data.  The fitted slope is the Weibull shape parameter β;\n",
    "the vertical dashed line marks the characteristic life η."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c9640830",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = weibull_plot(data_pos)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b71d60e4",
   "metadata": {},
   "source": [
    "## Probability Plot  (NIST 1.3.3.24)\n",
    "\n",
    "Generalisation of the normal probability plot: compare ordered data\n",
    "against the quantiles of any `scipy.stats` distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bfbe691c",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = probability_plot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "068a3e86",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = probability_plot(data, distribution=\"expon\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05cf1605",
   "metadata": {},
   "source": [
    "## Box-Cox Normality Plot  (NIST 1.3.3.8)\n",
    "\n",
    "Finds the Box-Cox power λ that maximises normality of positive data.\n",
    "The 2×2 grid shows the original histogram, the PPCC-vs-λ curve,\n",
    "the transformed histogram, and the normal probability plot of the\n",
    "transformed data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "97fcb669",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = box_cox_normality_plot(data_pos)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "597888b7",
   "metadata": {},
   "source": [
    "## Bootstrap Plot  (NIST 1.3.3.4)\n",
    "\n",
    "Resamples the data to approximate the sampling distribution of any\n",
    "statistic.  The histogram of the bootstrap distribution gives a\n",
    "non-parametric confidence interval for the statistic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7b5c483e",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = bootstrap_plot(data, n_bootstrap=500)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31338610",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = bootstrap_plot(data, statistic=np.median, n_bootstrap=500)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b67fe0a",
   "metadata": {},
   "source": [
    "## Box-Cox Linearity Plot  (NIST 1.3.3.9)\n",
    "\n",
    "Plots |corr(y, x^λ)| across a range of λ values to identify the power\n",
    "transformation of `x` that best linearises the relationship with `y`.\n",
    "Requires `x > 0`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07bf1a07",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_pos = np.linspace(0.1, 10.0, 50)\n",
    "y_lin = 3.0 * x_pos**0.5 + rng.normal(scale=0.5, size=50)\n",
    "data_lin = EDAData(y=y_lin, x=x_pos)\n",
    "\n",
    "fig, ax = box_cox_linearity_plot(data_lin)\n",
    "plt.show()"
   ]
  }
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