wahrscheinlichkeitsverteilungen.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Wahrscheinlichkeitsverteilungen\n",
    "\n",
    "**Verschiedene Verteilungsfunktionen interaktiv visualisieren**\n",
    "\n",
    "Verschiedene Funktionen können ausgewählt werden und interaktiv dargestellt erden.\n",
    "\n",
    "Funktionen:\n",
    "- Poissonverteilung, [scipy-link](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.poisson.html#scipy.stats.poisson)\n",
    "- Gamma - Poisson Verteilung, [scipy-link](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.nbinom.html#scipy.stats.nbinom)\n",
    "- Binomialverteilung, [scipy-link](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.binom.html#scipy.stats.binom)\n",
    "- Dichtefunktion (Gauss - Funktion), [scipy-link](https://docs.scipy.org/doc/scipy-0.16.1/reference/generated/scipy.stats.norm.html)\n",
    "- Landauverteilung, [scipy-link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.moyal.html)\n",
    "- Gamma - Verteilung, [scipy-link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html#scipy.stats.gamma)\n",
    "- Weibullverteilung, [scipy-link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_min.html#scipy.stats.weibull_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "lang": "en"
   },
   "outputs": [],
   "source": [
    "# resourcen\n",
    "import ipywidgets as widgets\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.stats import poisson, gamma, moyal, norm, binom, nbinom, weibull_min\n",
    "\n",
    "#set backend for interactive toolbar\n",
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# während der Berechnung der Verteilungen werden Warnungen ausgegeben.\n",
    "# Diese werden hier ausgeschalten\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# interaktive Schalter\n",
    "#\n",
    "# Signalauswahl\n",
    "distribFuns = ['Poisson-Verteilung', 'Gamma-Poisson-Verteilung',\n",
    "               'Binomialverteilung','Normalverteilung','Landau-Verteilung',\n",
    "               'Gamma-Verteilung','Weibull-Verteilung']\n",
    "distrib_select = widgets.Dropdown(description='', options=distribFuns,\n",
    "                                  value='Normalverteilung',\n",
    "                                  layout= widgets.Layout(width='55%',height='auto')\n",
    "                                 )\n",
    "#----------------------------------------------------------------------------------\n",
    "layout= widgets.Layout(width='95%',height='auto')\n",
    "style = {'description_width': 'initial'}\n",
    "# Funktionsparameter\n",
    "# ------------------------------------------------------------------------------------------------------------------------------\n",
    "#\n",
    "# Gauss: µ: Erwartungswert, \\sigma: Standardabweichung \n",
    "mu = widgets.FloatSlider(min=-150, max=150, value=0, continuous_update=False, layout= layout)\n",
    "sigma = widgets.FloatSlider(min=0.1, max=15, value=1, layout= layout)\n",
    "#\n",
    "normLabel_1 = \"µ: (Erwartungswert)\"\n",
    "normLabel_2 = \"$\\sigma$: (Standardabweichung)\"\n",
    "\n",
    "# ------------------------------------------------------------------------------------------------------------------------------\n",
    "#\n",
    "# Poisson: Erwartungswert und Varianz µ (geteilt mit Gauss - Erwartungswert), µ > 0 \n",
    "poisLabel = \"µ: (Erwartungswert und Varianz)\"\n",
    "# # ------------------------------------------------------------------------------------------------------------------------------\n",
    "## Gamma-Poisson => negative Binomialverteilung: \n",
    "#                  n: Anzahl Erfolge, alternativ über µ einstellbar n = (µ²/{\\sigma}² - µ)\n",
    "#                  p: Einzelwahrscheinlichkeit , alternativ über µ und sigma einstellbar: p= (µ/{\\sigma}²)\n",
    "#\n",
    "gammaPoisLabel_1 = \"n: (Anzahl der Erfolge n. n > 0 ($mean²\\over (var - mean)$)\"\n",
    "gammaPoisLabel_2 = \"p: (Wahrscheinlichkeit eines einzelnen Erfolgs. $0 \\leq p \\leq 1$ (mean/varianz)\"\n",
    "\n",
    "# ----------------------------------------------------------------------------------------------------------------------------\n",
    "#\n",
    "# Binomialverteilung: n: Anzahl der Erfolger, p: Einzelwahrscheinlichkeit\n",
    "# (Schaltflächen mit Gamma-Poisson-Verteilung geteilt)\n",
    "#\n",
    "binomLabel_1 = \"n: (Anzahl der Erfolge n. n > 0 (mean²/(var - mean))\"\n",
    "binomLabel_2 = \"p: (Wahrscheinlichkeit eines einzelnen Erfolgs. $0 \\leq p \\leq 1$ (mean/varianz)\"\n",
    "\n",
    "# ----------------------------------------------------------------------------------------------------------------------------\n",
    "#\n",
    "# Landauverteilung: Lageparameter µ ; Skalenparameter c\n",
    "# (Schaltflächen mit Normalverteilung und Poisson-Verteilung geteilt)\n",
    "landauLabel_1 = \"µ: (Erwartungswert)\"\n",
    "landauLabel_2 = \"$\\sigma$: (Standardabweichung)\"\n",
    "\n",
    "# ----------------------------------------------------------------------------------------------------------------------------\n",
    "#\n",
    "# Gammaverteilung: inverser Skalenparameter b; Formparameter p\n",
    "# ----------------------------------------------------------------------------------------------------------------------------\n",
    "p_gamma = widgets.FloatSlider(min=0, max=150, value=1, step=0.01, continuous_update=False, layout= layout)\n",
    "#\n",
    "gammaLabel_1 = \"p: Formparater (p>0)\"\n",
    "gammaLabel_2 = \"b: (Skalierungsfaktor)\"\n",
    "gammaLabel_3 = \"µ: (Mittelwert)\"\n",
    "#\n",
    "# ----------------------------------------------------------------------------------------------------------------------------\n",
    "#\n",
    "# Weibull : - Skalen- und Formparameter:\n",
    "#           1/lambda > 0\n",
    "wblLabel_1 = \"k: Formparater (k > 0)\"\n",
    "wblLabel_2 = \"$\\lambda$: (Skalenparameter $\\lambda$.$1 \\over \\lambda > 0$.)\"\n",
    "wblLabel_3 = \"µ: (Verschiebeoperator)\"\n",
    "#\n",
    "# ---------------------------------------------------------------------------------------------------------------------------\n",
    "# interaktive Schaltflächen in widget 'interakt' zusammengefasst\n",
    "# - zu jeder gewählten Verteilungsfunktion werden die Schaltflächen angepasst\n",
    "#\n",
    "label_1 = widgets.Label(vlaue=\"\", tooltips=\"\")\n",
    "label_2 = widgets.Label(vlaue=\"\", tooltips=\"\")\n",
    "label_3 = widgets.Label(vlaue=\"\", tooltips=\"\")\n",
    "\n",
    "interakt = widgets.VBox([\\\n",
    "                         label_1,\n",
    "                         widgets.FloatSlider(min=0.1, max=1.0,continuous_update=False),\n",
    "                         label_2,\n",
    "                         widgets.FloatSlider(min = 0.0, max=1.1, continuous_update=False),\n",
    "                         label_3,\n",
    "                         widgets.FloatSlider(min=0.1,max=1.1, continuous_update=False)\n",
    "                        ]\n",
    "                       )\n",
    "# plot limits\n",
    "x_range = widgets.IntRangeSlider(min= -200, max=200, value=[-5,5], continuous_update=False)\n",
    "xrangeBox = widgets.VBox([\n",
    "    widgets.Label(value=\"x-range\"),\n",
    "    x_range\n",
    "])\n",
    "#\n",
    "BtnReset = widgets.Button(description=\"reset\", button_style='warning')\n",
    "# ---------------------------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_ProbabilityDensity(x, f_distribution, ax):\n",
    "    ax.clear()\n",
    "    ax.set_title(\"Dichtefunktion zur {}\".format(distrib_select.value))\n",
    "    #Verteilung nochmal zeichnen und dann die entsprechenden Informationen eintragen\n",
    "    if distrib_select.value in ['Poisson-Verteilung', 'Gamma-Poisson-Verteilung', 'Binomialverteilung']:\n",
    "        ax.bar(x, f_distribution, color='green', width=0.25)\n",
    "    else:\n",
    "        ax.plot(x, f_distribution, color='green', lw=2)\n",
    "        ax.fill_between(x, 0, f_distribution, where =(f_distribution >= 0),\\\n",
    "                   facecolor='green', alpha=0.3)\n",
    "    # Abszissenbereich entsprechend Bereichsauswahl einstellen\n",
    "    ax.set_xlim(x_range.value[0], x_range.value[-1])\n",
    "    ax.set_xlabel(\"x\")\n",
    "    ax.set_ylabel(\"Wahrscheinlichkeit\")\n",
    "    #\n",
    "    # Gitterlinien andeuten\n",
    "    ax.yaxis.grid(True, linestyle='-', which='major', color='lightgrey',\n",
    "               alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_cumulativeProbability(x, f_distribution, ax):\n",
    "    ax.clear()\n",
    "    ax.set_title(\"kumulative Verteilung zur {}\".format(distrib_select.value))\n",
    "    ax.plot(x, f_distribution, color='C1', lw=2)\n",
    "    ax.fill_between(x, 0, f_distribution, where =(f_distribution >= 0),\\\n",
    "                   facecolor='C1', alpha=0.3)\n",
    "    # Abszissenbereich entsprechend Bereichsauswahl einstellen\n",
    "    ax.set_xlim(x_range.value[0], x_range.value[-1])\n",
    "    ax.set_xlabel(\"x\")\n",
    "    ax.set_ylabel(\"Wahrscheinlichkeit\")\n",
    "    # Gitterlinien andeuten\n",
    "    ax.yaxis.grid(True, linestyle='-', which='major', color='lightgrey',\n",
    "               alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def reset_controls(*btn):\n",
    "    # Reset Button:\n",
    "    global interakt\n",
    "    distrib_select.value = 'Normalverteilung'\n",
    "    interakt.children[0].value = normLabel_1\n",
    "    interakt.children[2].value = normLabel_2\n",
    "    interakt.children[1].disabled = False\n",
    "    interakt.children[1].min = -150\n",
    "    interakt.children[1].max = 150\n",
    "    interakt.children[1].style.handle_color = \"green\"\n",
    "    interakt.children[1].value = 0.0\n",
    "    interakt.children[3].disabled = False\n",
    "    interakt.children[3].min = 0.01\n",
    "    interakt.children[3].max = 50\n",
    "    interakt.children[3].value = 1\n",
    "    interakt.children[3].step = 0.05\n",
    "    interakt.children[3].style.handle_color = \"green\"\n",
    "    interakt.children[4].disabled = True\n",
    "    interakt.children[4].value = \"\"\n",
    "    interakt.children[4].disabled = True\n",
    "    interakt.children[4].value = \"\"\n",
    "    x_range.value = [-5,5]\n",
    "    update_view()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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     "output_type": "display_data"
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       "VBox(children=(HBox(children=(VBox(children=(Label(value='Funktionsauswahl:', layout=Layout(height='auto', wid…"
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   "source": [
    "# interaktive Visualisierung:\n",
    "#\n",
    "#- Figuren Zeichnen:\n",
    "fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(6,6))\n",
    "\n",
    "distribType_old = \"Poisson-Verteilung\"\n",
    "#\n",
    "# 1. create a callback which updates the plot when a control-value has changed\n",
    "def update_view(*args):\n",
    "    global distribType_old\n",
    "    global interakt\n",
    "    \n",
    "    # selections\n",
    "    distribType = distrib_select.value\n",
    "    \n",
    "    initWidgets = True\n",
    "    if distribType == distribType_old:\n",
    "        initWidgets = False\n",
    "    #-----------------------------------------------------------\n",
    "    # Datensatz nach der gewählten Verteilungsfunktion erzeugen\n",
    "    #   \n",
    "    # abszisse: ppf({...}}) Percent point function (inverse of cdf — percentiles).\n",
    "    # Dichtefunktion/Wahrscheinlichkeitsfunktion: pdf({...}})/pmf({...}})\n",
    "    # kummulierte Dichtefunktion: cdf({...}}) Cumulative density function.\n",
    "    #\n",
    "    if (distribType == \"Normalverteilung\"):\n",
    "        if initWidgets:\n",
    "            # init intaeraktWidget\n",
    "            interakt.children[0].value = normLabel_1\n",
    "            interakt.children[2].value = normLabel_2\n",
    "            interakt.children[1].disabled = False\n",
    "            interakt.children[1].min = -150\n",
    "            interakt.children[1].max = 150\n",
    "            interakt.children[1].style.handle_color = \"green\"\n",
    "            interakt.children[1].value = 0.0\n",
    "            interakt.children[3].disabled = False\n",
    "            interakt.children[3].min = 0.01\n",
    "            interakt.children[3].max = 50\n",
    "            interakt.children[3].value = 1\n",
    "            interakt.children[3].step = 0.05\n",
    "            interakt.children[3].style.handle_color = \"green\"\n",
    "            interakt.children[4].disabled = True\n",
    "            interakt.children[4].value = \"\"\n",
    "            interakt.children[4].disabled = True\n",
    "            interakt.children[4].value = \"\"\n",
    "            #\n",
    "        mu= interakt.children[1].value\n",
    "        sigma = interakt.children[3].value\n",
    "        #\n",
    "        x_dist = np.arange(norm.ppf(0.01, mu, sigma), norm.ppf(0.99, mu, sigma), 1/100)\n",
    "        distrib_f = norm(mu, sigma)\n",
    "        #\n",
    "        dist_prob = distrib_f.pdf(x_dist)\n",
    "        dist_cdf = distrib_f.cdf(x_dist)\n",
    "#------------------------------------------------           \n",
    "    if (distribType == \"Poisson-Verteilung\"):\n",
    "        if initWidgets:\n",
    "            x_range.min = 0\n",
    "            # init intaeraktWidget\n",
    "            interakt.children[0].value = poisLabel\n",
    "            interakt.children[1].disabled = False\n",
    "            interakt.children[1].min = 0.1\n",
    "            interakt.children[1].style.handle_color = \"green\"\n",
    "            interakt.children[1].value = 3.76\n",
    "            interakt.children[2].disabled = True\n",
    "            interakt.children[2].value = \"\"\n",
    "            interakt.children[3].style.handle_color = None\n",
    "            interakt.children[3].disabled = True\n",
    "            interakt.children[4].disabled = True\n",
    "            interakt.children[4].value = \"\"\n",
    "            interakt.children[4].disabled = True\n",
    "            interakt.children[5].style.handle_color = None\n",
    "            interakt.children[5].disabled = True\n",
    "            #\n",
    "        mu = interakt.children[1].value\n",
    "        x_dist = np.arange(poisson.ppf(0.001, mu), poisson.ppf(0.999, mu))\n",
    "        dist_prob = poisson.pmf(x_dist, mu)\n",
    "        dist_cdf = poisson.cdf(x_dist, mu)\n",
    "#--------------------------------------------------------       \n",
    "    if (distribType == \"Gamma-Poisson-Verteilung\"):\n",
    "        if initWidgets:\n",
    "        # Diagram-Bereich umschalten damit Funktion sichtbar\n",
    "            x_range.min = 0\n",
    "            # init intaeraktWidget\n",
    "            interakt.children[0].disabled = False\n",
    "            interakt.children[0].value = gammaPoisLabel_1\n",
    "            interakt.children[1].disabled = False\n",
    "            interakt.children[1].style.handle_color = \"green\"\n",
    "            interakt.children[1].min = 1\n",
    "            interakt.children[1].max = 500\n",
    "            interakt.children[1].value = 10\n",
    "            interakt.children[1].step = 1.0\n",
    "            interakt.children[2].disabled = False\n",
    "            interakt.children[2].value = gammaPoisLabel_2\n",
    "            interakt.children[3].disabled = False\n",
    "            interakt.children[3].style.handle_color = \"green\"\n",
    "            interakt.children[3].min = 0\n",
    "            interakt.children[3].max = 1\n",
    "            interakt.children[3].value = 0.5\n",
    "            interakt.children[3].step = 0.05\n",
    "            interakt.children[4].disabled = True\n",
    "            interakt.children[4].value = \"\"\n",
    "            interakt.children[5].disabled = True\n",
    "            interakt.children[5].style.handle_color = None\n",
    "        n= interakt.children[1].value\n",
    "        p= interakt.children[3].value\n",
    "        x_dist = np.arange(nbinom.ppf(0.001, n, p), nbinom.ppf(0.999, n, p))\n",
    "        #\n",
    "        distrib_f = nbinom(n, p)\n",
    "        dist_prob = distrib_f.pmf(x_dist)\n",
    "        dist_cdf = distrib_f.cdf(x_dist)\n",
    "#------------------------------------------------------    \n",
    "    if (distribType == \"Binomialverteilung\"):\n",
    "        if initWidgets:\n",
    "            # Diagram-Bereich umschalten damit Funktion sichtbar\n",
    "            x_range.min = 0\n",
    "            # init intaeraktWidget\n",
    "            interakt.children[0].disabled = False\n",
    "            interakt.children[0].value = binomLabel_1\n",
    "            interakt.children[1].disabled = False\n",
    "            interakt.children[1].style.handle_color = \"green\"\n",
    "            interakt.children[1].min = 1\n",
    "            interakt.children[1].max = 500\n",
    "            interakt.children[1].value = 10\n",
    "            interakt.children[1].step = 1.0\n",
    "            interakt.children[2].disabled = False\n",
    "            interakt.children[2].value = binomLabel_2\n",
    "            interakt.children[3].disabled = False\n",
    "            interakt.children[3].style.handle_color = \"green\"\n",
    "            interakt.children[3].min = 0\n",
    "            interakt.children[3].max = 1\n",
    "            interakt.children[3].value = 0.5\n",
    "            interakt.children[3].step = 0.05\n",
    "            interakt.children[4].disabled = True\n",
    "            interakt.children[4].value = \"\"\n",
    "            interakt.children[5].disabled = True\n",
    "            interakt.children[5].style.handle_color = None\n",
    "        #\n",
    "        n= interakt.children[1].value\n",
    "        p= interakt.children[3].value\n",
    "        #\n",
    "        x_dist = np.arange(binom.ppf(0.01, n, p), binom.ppf(0.99, n, p))\n",
    "        distrib_f = binom(n, p)\n",
    "        dist_prob = distrib_f.pmf(x_dist)\n",
    "        dist_cdf = distrib_f.cdf(x_dist)\n",
    "#-----------------------------------------------------------        \n",
    "    if (distribType == \"Gamma-Verteilung\"):\n",
    "        if initWidgets:\n",
    "            # Diagram-Bereich umschalten damit Funktion sichtbar\n",
    "            x_range.min = 0\n",
    "            # init intaeraktWidget\n",
    "            interakt.children[0].disabled = False\n",
    "            interakt.children[0].value = gammaLabel_1\n",
    "            interakt.children[1].disabled = False\n",
    "            interakt.children[1].style.handle_color = \"green\"\n",
    "            interakt.children[1].min = 0\n",
    "            interakt.children[1].max = 150\n",
    "            interakt.children[1].value = 1\n",
    "            interakt.children[1].step = 0.05\n",
    "            interakt.children[2].disabled = False\n",
    "            interakt.children[2].value = gammaLabel_2\n",
    "            interakt.children[3].disabled = False\n",
    "            interakt.children[3].style.handle_color = \"green\"\n",
    "            interakt.children[3].min = 0\n",
    "            interakt.children[3].max = 15\n",
    "            interakt.children[3].value = 0.05\n",
    "            interakt.children[3].step = 0.05\n",
    "            interakt.children[4].disabled = False\n",
    "            interakt.children[4].value = gammaLabel_3\n",
    "            interakt.children[5].disabled = False\n",
    "            interakt.children[5].style.handle_color = \"green\"\n",
    "            interakt.children[5].min = 0\n",
    "            interakt.children[5].value = 0\n",
    "            interakt.children[5].step = 1.0\n",
    "            interakt.children[5].max = 150\n",
    "        #\n",
    "        p = interakt.children[1].value\n",
    "        sigma = interakt.children[3].value\n",
    "        mu = interakt.children[5].value\n",
    "        x_dist = np.arange(gamma.ppf(0.001, p, loc=mu), gamma.ppf(0.999, p, loc=mu), 1/100)\n",
    "        #\n",
    "        distrib_f = gamma(p, loc= mu, scale= sigma)\n",
    "        dist_prob = distrib_f.pdf(x_dist)\n",
    "        dist_cdf = distrib_f.cdf(x_dist)\n",
    "#----------------------------------------------------------\n",
    "\n",
    "    if (distribType == \"Landau-Verteilung\"):\n",
    "        if initWidgets:\n",
    "            # Diagram-Bereich umschalten damit Funktion sichtbar        \n",
    "            x_range.min = -10\n",
    "            # init intaeraktWidget\n",
    "            interakt.children[0].disabled = False\n",
    "            interakt.children[0].value = landauLabel_1\n",
    "            interakt.children[1].disabled = False\n",
    "            interakt.children[1].style.handle_color = \"green\"\n",
    "            interakt.children[1].min = -150\n",
    "            interakt.children[1].max = 150\n",
    "            interakt.children[1].value = 1\n",
    "            interakt.children[1].step = 0.1\n",
    "            interakt.children[2].disabled = False\n",
    "            interakt.children[2].value = landauLabel_2\n",
    "            interakt.children[3].disabled = False\n",
    "            interakt.children[3].style.handle_color = \"green\"\n",
    "            interakt.children[3].min = 0\n",
    "            interakt.children[3].max = 15\n",
    "            interakt.children[3].step = 0.05\n",
    "            interakt.children[4].disabled = True\n",
    "            interakt.children[4].value = \"\"\n",
    "            interakt.children[5].disabled = True\n",
    "            interakt.children[5].style.handle_color = None\n",
    "            interakt.children[5].min = 0\n",
    "            interakt.children[5].value = 0\n",
    "        #\n",
    "        mu = interakt.children[1].value\n",
    "        sigma = interakt.children[3].value\n",
    "        x_dist = np.arange(moyal.ppf(0.001), moyal.ppf(0.999), 1/100)\n",
    "        #\n",
    "        dist_prob = moyal.pdf(x_dist,loc=mu, scale=sigma)\n",
    "        dist_cdf = moyal.cdf(x_dist,loc=mu, scale=sigma)\n",
    "#--------------------------------------------------------\n",
    "    if (distribType == \"Weibull-Verteilung\"):\n",
    "        if initWidgets:\n",
    "            # init intaeraktWidget\n",
    "            interakt.children[1].disabled = False\n",
    "            interakt.children[1].style.handle_color = \"green\"\n",
    "            interakt.children[1].min = 0.1\n",
    "            interakt.children[1].max = 15\n",
    "            interakt.children[1].value = 1.69\n",
    "            interakt.children[1].step = 0.05\n",
    "            interakt.children[2].disabled = False\n",
    "            interakt.children[2].value = wblLabel_2\n",
    "            interakt.children[3].disabled = False\n",
    "            interakt.children[3].style.handle_color = \"green\"\n",
    "            interakt.children[3].min = 0.01\n",
    "            interakt.children[3].max = 100\n",
    "            interakt.children[3].value = 1\n",
    "            interakt.children[3].step = 0.05\n",
    "            interakt.children[4].disabled = False\n",
    "            interakt.children[4].value = wblLabel_3\n",
    "            interakt.children[5].disabled = False\n",
    "            interakt.children[5].style.handle_color = \"green\"\n",
    "            interakt.children[5].min = 0\n",
    "            interakt.children[5].value = 0\n",
    "            interakt.children[5].step = 0.5\n",
    "            interakt.children[5].max = 150\n",
    "        #\n",
    "        form_wbl = interakt.children[1].value\n",
    "        lambda_wbl = interakt.children[3].value\n",
    "        mu = interakt.children[5].value\n",
    "        x_dist = np.linspace(weibull_min.ppf(0.01, form_wbl, loc= mu), weibull_min.ppf(0.99, form_wbl, loc=mu),100)\n",
    "        distrib_f = weibull_min(form_wbl, scale=lambda_wbl, loc= mu)\n",
    "        #\n",
    "        dist_prob = distrib_f.pdf(x_dist)\n",
    "        dist_cdf = distrib_f.cdf(x_dist)\n",
    "#---------------------------------------------------------------------------\n",
    "# diagramme aktualisieren\n",
    "#\n",
    "#\n",
    "    draw_ProbabilityDensity(x_dist, dist_prob, axes[0])\n",
    "    draw_cumulativeProbability(x_dist, dist_cdf, axes[1])\n",
    "    \n",
    "    distribType_old = distribType\n",
    "    #\n",
    "    fig.tight_layout()\n",
    "    #  \n",
    "#--------------------------------------------------------\n",
    "# 2. die Callback-Funktion mit der Funktion 'observe' den Steuerelementen zuweisen\n",
    "    \n",
    "distrib_select.observe(update_view, 'value')\n",
    "x_range.observe(update_view, 'value')\n",
    "interakt.children[1].observe(update_view, 'value')\n",
    "interakt.children[3].observe(update_view, 'value')\n",
    "interakt.children[5].observe(update_view, 'value')\n",
    "BtnReset.on_click(reset_controls)\n",
    "#--------------------------------------------------------\n",
    "# Anwendung starten\n",
    "#\n",
    "# Diagramme einmal zeichnen\n",
    "update_view()\n",
    "#\n",
    "# mit 'widgets.VBox / .HBox' die Steuerelemente arangieren\n",
    "widgets.VBox([\n",
    "    widgets.HBox([\n",
    "        widgets.VBox([\n",
    "            widgets.Label(value=\"Funktionsauswahl:\", layout= widgets.Layout(width='55%',height='auto')),\n",
    "            distrib_select,\n",
    "            widgets.HTML(value=\"<hr>\")\n",
    "            ],\n",
    "            layout={'width': '30%'}\n",
    "        ),\n",
    "        widgets.VBox([\n",
    "            interakt,\n",
    "            xrangeBox,\n",
    "        ],\n",
    "            layout={'width': '50%'}\n",
    "        )\n",
    "        ]),\n",
    "    widgets.HTML(value=\"<hr>\"),\n",
    "    BtnReset\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Erläuterungen zur interaktiven Nutzung**\n",
    "<br>\n",
    "<br>\n",
    "Funktionsauswahl: $\\quad$ Funktion auswaehlen. Bei Funktionsaenderung werden default-Parameter eingestellt.<br>\n",
    "Schieberegler: $\\qquad$ Einstellungen zur gewählten Funktion. Parameter werden entsprechend der gewählten Funktion bezeichnet und freigeschalten.<br>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright © 2020 IUBH Internationale Hochschule"
   ]
  }
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