{ "metadata": { "name": "", "signature": "sha256:4f4058afba6d23a748075da8b6a9145cfc36337e09fb59defca687ca601a7602" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": true, "input": [ "from pylab import *\n", "from scipy import stats\n", "%matplotlib inline\n", "\n", "# nastavitve za izris grafov (http://matplotlib.org/1.3.1/users/customizing.html)\n", "rc('text', usetex=True)\n", "rc('font', size=12, family='serif', serif=['Computer Modern'])\n", "rc('xtick', labelsize='small')\n", "rc('ytick', labelsize='small')\n", "rc('legend', frameon=False, fontsize='medium')\n", "rc('figure', figsize=(5, 3))\n", "rc('lines', linewidth=2.0)\n", "rc('axes', color_cycle=['k'])\n", "\n", "# \u0161tevilo predal\u010dkov v histogramu (pravilo Freedmana in Diakonisa)\n", "def stevilo_predalckov(x):\n", " iqr = percentile(x, 75) - percentile(x, 25)\n", " sirina = 2.0 * iqr * len(x) ** (-1.0 / 3.0)\n", " return int((max(x) - min(x)) / sirina) \n", "\n", "# Gaussova porazdelitev\n", "gauss=lambda x, m, s: (1 / (s * sqrt(2 * pi)) * exp(-0.5 * ((x - m) / s) ** 2))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Povpre\u010dja" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Porazdelitev vrednosti spremenljivke je lahko zelo pestra in bogata, kot smo videli na na\u0161ih zgledih. Kadar si ho\u010demo to sliko poenostaviti na nekaj \u0161tevilskih parametrov, zelo pogosto uporabljamo povpre\u010dja." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Kot zgled najprej nara\u010dunamo 1000 dogodkov (dogodek je spet vsota 100 metov kocke) in nari\u0161emo histogram verjetnostne gostote dogodkov:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# dogodek1 = vsota 100 metov kock\n", "def dogodek1():\n", " # izra\u010dunaj vsoto 100 naklju\u010dnih celih \u0161tevil med 1 in 6\n", " return sum(randint(1, 7, 100))\n", "\n", "# N dogodkov1\n", "def N_dogodkov1(N):\n", " # izra\u010dunaj N naklju\u010dnih dogodkov\n", " return [dogodek1() for i in xrange(N)]\n", "\n", "dogodki1=N_dogodkov1(1000)\n", "\n", "figure(figsize=(10,3));\n", "subplot(121);\n", "plot(dogodki1, '.');\n", "xlabel(r'Zaporedna \\v st. dogodka');\n", "ylabel(r'Vsota 100 metov kocke');\n", "subplot(122);\n", "hist(dogodki1, stevilo_predalckov(dogodki1), normed=True, alpha=0.5);\n", "xlabel(r'Vsota 100 metov kocke');\n", "ylabel(r'Verjetnostna gostota');\n", "tight_layout();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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AwNNKjJbLFBcXw+/3AwAGBwexatUq5Xrbt2/n/66urkZ1dbWtYyIIghgvx48f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\n6O3tRTQazaZdBDElUEUnp+osxUTaPZ7odC4j27ls3bxhwwY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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Porazdelitev bomo opisali s tremi parametri ($N$ je \u0161tevilo izmerjenih vrednosti, $x_i$ so posamezne izmerjene vrednosti):\n", "\n", "Koeficienta $C_\\sigma$ in $C_\\gamma$ poskrbita za popravek, ker obravnavamo samo naklju\u010dni vzorec (ang. sample) $N$-tih vrednosti iz porazdelitve. \u010ce imamo na voljo celotno porazdelitev, sta $C_\\sigma=C_\\gamma=1$. V tem primeru dobimo prave vrednosti povpre\u010dja, standardnega odklona in po\u0161evnosti porazdelitve (ang. population mean, ...) \n", "\n", "\n", "Za spremenljivko, ki smo ji dolo\u010dili $\\bar x$ in $\\sigma$, si v najbolj grobem pribli\u017eku predstavljamo, da je porazdeljena po Gaussovi (normalni) porazdelitvi $G(x)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}e^{-\\frac{\\left(x-\\bar x\\right)^2}{2\\sigma^2}}$. Ta je simetri\u010dna glede na vrh pri $x=\\bar x$, njena po\u0161evnost je torej enaka 0. Kljub temu lahko pri kon\u010dnem \u0161tevilu meritev ocena po\u0161evnosti odstopa od te teoreti\u010dne vrednosti tudi za spremenljivko, katere porazdelitev je Gaussova. Teorija pove, da lahko z veliko gotovostjo (pribli\u017eno 95%) trdimo, da porazdelitev ni Gaussova, \u010de je $\\left|\\gamma\\right|>2\\sigma_\\gamma$, kjer je $\\sigma_\\gamma=\\sqrt\\frac{6N(N-1)}{(N-2)(N+1)(N+3)}$.\n", "\n", "\n", "Podobno je s povpre\u010djem porazdelitve. Ocene povpre\u010dja vzorca iz Gaussove porazdelitve so okoli pravega povpre\u010dja porazdeljene, standardni odklon te porazdelitve je $\\sigma_\\bar x=\\frac{\\sigma}{\\sqrt{N}}$. Ta izraz lahko uporabimo kot oceno napake izra\u010dunanega povpre\u010dja (ang. standard error of the mean). Vidimo, da kvaliteta ocene povpre\u010dja nara\u0161\u010da s pove\u010devanjem \u0161tevila meritev. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Izra\u010dunajmo torej parametre porazdelitve na\u0161ih dogodkov in nari\u0161imo pripadajo\u010do Gaussovo porazdelitev (rde\u010da \u010drta):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "N=len(dogodki1)\n", "print \"Ocena povpre\u010dja:\", stats.tmean(dogodki1)\n", "print \"Ocena napake povpre\u010dja:\", stats.sem(dogodki1)\n", "print \"Ocena standardnega odklona:\", stats.tstd(dogodki1)\n", "print \"Ocena po\u0161evnosti:\", stats.skew(dogodki1, bias=False)\n", "print \"Standardni odklon porazdelitve po\u0161evnosti za Gaussovo porazdelitev:\", sqrt(6.0 * N * (N - 1) / (N - 2) / (N + 1) / (N + 3))\n", "\n", "ax=subplot()\n", "hist(dogodki1, stevilo_predalckov(dogodki1), normed=True, alpha=0.5);\n", "gauss=lambda x, m, s: (1 / (s * sqrt(2 * pi)) * exp(-0.5 * ((x - m) / s) ** 2))\n", "x=linspace(100, 600, 1000);\n", "ax.set_autoscalex_on(False)\n", "plot(x, gauss(x, stats.tmean(dogodki1), stats.tstd(dogodki1)), 'r')\n", "xlabel(r'Vsota 100 metov kocke');\n", "ylabel(r'Verjetnostna gostota');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Ocena povpre\u010dja: 349.62\n", "Ocena napake povpre\u010dja: 0.533948219119\n", "Ocena standardnega odklona: 16.8849252501\n", "Ocena po\u0161evnosti: -0.0386095275642\n", "Standardni odklon porazdelitve po\u0161evnosti za Gaussovo porazdelitev: 0.0773438156196\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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MZNL16yzrrB8hlBU2wW7cuJHGxsbQ75s2baKqqmrApQpNJhNWqxVTcKnnAezv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\nZ6PVahUbMxscVgaBfyzLli2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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Na kratko: povpre\u010dje porazdelitve je $349.6\\pm0.5$, njen standardni odklon pa $16.9$. Porazdelitev ni po\u0161evna." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Poglejmo si \u0161e, kako so porazdeljena povpre\u010dja in po\u0161evnosti 1000 vzorcev (vsak vzorec vsebuje po 1000 dogodkov). Vidimo, da je \u0161irino obeh porazdelitev dobro opi\u0161eta zgoraj izra\u010dunani vrednosti." ] }, { "cell_type": "code", "collapsed": false, "input": [ "povprecja=[stats.tmean(N_dogodkov1(1000)) for i in xrange(1000)];\n", "posevnosti=[stats.skew(N_dogodkov1(1000)) for i in xrange(1000)];\n", "figure(figsize=(10, 3));\n", "subplot(121);\n", "hist(povprecja, stevilo_predalckov(povprecja), normed=True, alpha=0.5);\n", "xlabel(r'Povpre\\v cje vzorca 1000 dogodkov');\n", "ylabel(r'Verjetnostna gostota');\n", "subplot(122);\n", "hist(posevnosti, stevilo_predalckov(posevnosti), normed=True, alpha=0.5);\n", "xlabel(r'Po\\v sevnost vzorca 1000 dogodkov');\n", "ylabel(r'Verjetnostna gostota');\n", "tight_layout();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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mSqWS3Q1C0zR89913Q5/T6SOsKIr9WHfXCPYZJiJ6vHHyMxERtbkqiF+/fg1ZlgEArVYL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\nuL29dbTuX//1X2N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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ponovimo zdaj ra\u010dun za porazdelitev druga\u010dnih dogodkov (harmoni\u010dno povpre\u010dje 10 metov kocke):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# dogodek2 = harmoni\u010dno povpre\u010dje 10 metov kocke\n", "def dogodek2():\n", " # izra\u010dunaj hamoni\u010dno povpre\u010dje 10 naklju\u010dnih celih \u0161tevil med 1 in 6\n", " return stats.hmean(randint(1, 7, 10))\n", "\n", "# N dogodkov2\n", "def N_dogodkov2(N):\n", " # izra\u010dunaj N naklju\u010dnih dogodkov\n", " return [dogodek2() for i in xrange(N)]\n", "\n", "dogodki2=N_dogodkov2(1000)\n", "\n", "figure(figsize=(10,3));\n", "subplot(121);\n", "plot(dogodki2, '.');\n", "xlabel(r'Zaporedna \\v st. dogodka');\n", "ylabel(r'Harm. povpr. 10 metov kocke');\n", "subplot(122);\n", "hist(dogodki2, stevilo_predalckov(dogodki2), normed=True, alpha=0.5);\n", "xlabel(r'Harm. povpr. 10 metov kocke');\n", "ylabel(r'Verjetnostna gostota');\n", "tight_layout();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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DIm7ndDpRUVEBl8uF8fFxU4ckW85lOveTSf1hkVRtNrLT7rjpGkeGXaUO1blP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\nAUg1TUPvTK9atUpZsUG0bc+ePfD5fLY7iLHucoA8NUDFsUx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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "N=len(dogodki2)\n", "print \"Ocena povpre\u010dje:\", stats.tmean(dogodki2)\n", "print \"Ocena napake povpre\u010dja:\", stats.sem(dogodki2)\n", "print \"Ocena standardnega odklona:\", stats.tstd(dogodki2)\n", "print \"Ocena po\u0161evnosti:\", stats.skew(dogodki2, bias=False)\n", "print \"Standardni odklon porazdelitve po\u0161evnosti za Gaussovo porazdelitev:\", sqrt(6.0 * N * (N - 1) / (N - 2) / (N + 1) / (N + 3))\n", "\n", "ax=subplot()\n", "hist(dogodki2, stevilo_predalckov(dogodki2), normed=True, alpha=0.5);\n", "gauss=lambda x, m, s: (1 / (s * sqrt(2 * pi)) * exp(-0.5 * ((x - m) / s) ** 2))\n", "x=linspace(1, 6, 1000);\n", "ax.set_autoscalex_on(False)\n", "plot(x, gauss(x, stats.tmean(dogodki2), stats.tstd(dogodki2)), 'r')\n", "xlabel(r'Harm. povpr. 10 metov kocke');\n", "ylabel(r'Verjetnostna gostota');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Ocena povpre\u010dje: 2.59144556051\n", "Ocena napake povpre\u010dja: 0.0190889471981\n", "Ocena standardnega odklona: 0.603645512808\n", "Ocena po\u0161evnosti: 0.985425840089\n", "Standardni odklon porazdelitve po\u0161evnosti za Gaussovo porazdelitev: 0.0773438156196\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vidimo, da je ocenjena po\u0161evnost porazdelitve prevelika, da bi porazdelitev lahko bila Gaussova. Pozitivna po\u0161evnost se ka\u017ee v tem, da je desni rep porazdelitve dalj\u0161i. Na kratko: povpre\u010dje porazdelitve je $2.59\\pm0.02$, njen standardni odklon je $0.60$, po\u0161evnost pa $1.0$." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Naloge" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "
  1. Oceni povpre\u010dje, napako povpre\u010dja, standardni odklon in po\u0161evnost za spremenljivko v podatkih Ozadje.dat, ki prikazujejo rezultate meritve absorpcije rentgenskih \u017earkov (logaritem razmerja vpadnega in prepu\u0161\u010denega toka, drugi stolpec) brez merjenca, tako da pri\u010dakujemo konstantne ali skoraj konstantne vrednosti. Primerjaj histogram verjetnostne gostote z grafom Gaussove porazdelitve z enakim povpre\u010djem in standardnim odklonom. Lahko trdi\u0161, da porazdelitev ni Gaussova?\n", "\n", "
  2. V datoteki Maribor.zip so zbrani vremenski podatki z merilne postaje Maribor-letali\u0161\u010de za obdobje od 1. 1. 1977 do 31. 1. 2015. Ponovi postopek iz 1. naloge za povpre\u010dno dnevno temperaturo (datoteka TG_STAID003331.txt) v tem obdobju. \n", "\n", "
  3. Oceni povpre\u010dje in standardni odklon porazdelitve vsote vrednosti pri metu dveh kock tako, da z generatorjem naklju\u010dnih \u0161tevil generira\u0161 $10^6$ metov dveh kock. Parametra poskusi oceniti brez shranjevanja vrednosti v tabelo. Namig: $\\frac{1}{N}\\sum_{i=1}^N(x_i-\\bar x)^2=\\frac{1}{N}\\sum_{i=1}^N x_i^2-{\\bar x}^2$. Koliko oceni odstopata od teoreti\u010dnih vrednosti? \n", "
" ] } ], "metadata": {} } ] }