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‎variance_calc_examples.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "8266c456-f304-442e-97f6-a41659b3eef7",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'\\nvariance\\nmethods for calculating variance, including some of the latest techniques from research and scholarly articles.\\nmethods provide a variety of ways to calculate variance, each with its own advantages in terms of numerical stability and efficiency.\\n'"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"'''\n",
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"variance\n",
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"methods for calculating variance, including some of the latest techniques from research and scholarly articles.\n",
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"methods provide a variety of ways to calculate variance, each with its own advantages in terms of numerical stability and efficiency.\n",
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"'''"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "41fa44c8-e4f9-468b-9df9-431aa9fb4568",
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"metadata": {},
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"outputs": [],
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"source": [
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"def naive_variance(data):\n",
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" n = len(data)\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" mean = sum(data) / n\n",
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" variance = sum((x - mean) ** 2 for x in data) / (n - 1)\n",
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" return variance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "b466bebd-ec93-43d1-8650-6953266c3b3c",
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"metadata": {},
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"outputs": [],
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"source": [
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"def two_pass_variance(data):\n",
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" n = len(data)\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" mean = sum(data) / n\n",
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" variance = sum((x - mean) ** 2 for x in data) / n\n",
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" return variance\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "abbd8ba7-1b7f-4975-b321-5ae332ea02c5",
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"metadata": {},
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"outputs": [],
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"source": [
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"def welford_online(data):\n",
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" n = 0\n",
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" mean = 0\n",
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" M2 = 0\n",
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" for x in data:\n",
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" n += 1\n",
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" delta = x - mean\n",
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" mean += delta / n\n",
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" delta2 = x - mean\n",
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" M2 += delta * delta2\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" variance = M2 / (n - 1)\n",
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" return variance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "4c140d97-0ed0-404a-bc3c-354216fd5ab8",
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"metadata": {},
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"outputs": [],
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"source": [
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"def online_compensated(data):\n",
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" n = 0\n",
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" mean = 0\n",
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" M2 = 0\n",
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" for x in data:\n",
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" n += 1\n",
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" delta = x - mean\n",
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" mean += delta / n\n",
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" delta2 = x - mean\n",
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" M2 += delta * delta2\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" variance = M2 / (n - 1)\n",
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" return variance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"id": "ece7b688-850c-4190-9b8a-ab70f4efde9f",
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"metadata": {},
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"outputs": [],
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"source": [
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"def incremental_variance(data):\n",
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" n = 0\n",
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" mean = 0\n",
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" M2 = 0\n",
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" for x in data:\n",
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" n += 1\n",
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" delta = x - mean\n",
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" mean += delta / n\n",
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" delta2 = x - mean\n",
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" M2 += delta * delta2\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" variance = M2 / (n - 1)\n",
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" return variance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"id": "51664d40-4d2b-4936-a0eb-d25151278df5",
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"metadata": {},
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"outputs": [],
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"source": [
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"def kahan_variance(data):\n",
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" n = len(data)\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" mean = 0\n",
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" M2 = 0\n",
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" for x in data:\n",
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" y = x - mean\n",
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" t = M2 + y * y - mean * y\n",
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" mean += (y - t) / n\n",
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" M2 = t\n",
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" variance = M2 / (n - 1)\n",
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" return variance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"id": "04d20b15-7328-4b86-a321-5ba63a119bfc",
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"metadata": {},
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"outputs": [],
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"source": [
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"def neumaier_variance(data):\n",
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" n = len(data)\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" mean = 0\n",
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" M2 = 0\n",
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" for x in data:\n",
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" y = x - mean\n",
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" t = M2 + y * y - mean * y\n",
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" mean += (y - t) / n\n",
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" M2 = t\n",
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" variance = M2 / (n - 1)\n",
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" return variance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"id": "b1817c0c-743e-42df-8bef-91409cefc2fa",
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"metadata": {},
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"outputs": [],
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"source": [
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"def welford_online(data):\n",
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" n = 0\n",
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" mean = 0\n",
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" M2 = 0\n",
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" for x in data:\n",
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" n += 1\n",
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" delta = x - mean\n",
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" mean += delta / n\n",
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" delta2 = x - mean\n",
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" M2 += delta * delta2\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" variance = M2 / (n - 1)\n",
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" return variance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"id": "d2694042-b6dd-4e17-87e4-4ca0c8841ce3",
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"metadata": {},
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"outputs": [],
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"source": [
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"def kahan_stable_variance(data):\n",
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" n = len(data)\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" mean = 0\n",
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" M2 = 0\n",
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" for x in data:\n",
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" y = x - mean\n",
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" t = M2 + y * y - mean * y\n",
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" mean += (y - t) / n\n",
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" M2 = t\n",
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" variance = M2 / (n - 1)\n",
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" return variance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"id": "afd6a943-7082-476d-b1b5-d582417341da",
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"metadata": {},
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"outputs": [],
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"source": [
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"def incremental_compensated_variance(data):\n",
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" n = 0\n",
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" mean = 0\n",
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" M2 = 0\n",
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" for x in data:\n",
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" n += 1\n",
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" delta = x - mean\n",
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" mean += delta / n\n",
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" delta2 = x - mean\n",
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" M2 += delta * delta2\n",
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" if n < 2:\n",
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" return float('nan')\n",
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" variance = M2 / (n - 1)\n",
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" return variance"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d189d644-c891-43bd-a06d-de0313abb8a0",
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"metadata": {},
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"execution_count": null,
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"id": "1af67d1b-b018-4a70-8f0f-6d7e733c57ff",
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"id": "2e11bd17-c3e5-446b-9b94-fefebba2256f",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"codemirror_mode": {
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"name": "ipython",
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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