{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mô tả dữ liệu\n",
    "- Dataset: [Dresses_Attribute_Sales](https://archive.ics.uci.edu/ml/datasets/Dresses_Attribute_Sales)\n",
    "- Associated Tasks: Classification, Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import all necessary library\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from pyspark.sql import SparkSession\n",
    "from pyspark.sql import functions as F\n",
    "from pyspark.sql.types import *\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# initialize Spark\n",
    "spark = SparkSession.builder \\\n",
    "                .master(\"local\") \\\n",
    "                .appName(\"Data description Spark\") \\\n",
    "                .getOrCreate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----------+-------+-------+------+----+------+--------+------------+---------+-------------+----------+----------+------------+--------------+\n",
      "|  Dress_ID|  Style|  Price|Rating|Size|Season|NeckLine|SleeveLength|waiseline|     Material|FabricType|Decoration|Pattern Type|Recommendation|\n",
      "+----------+-------+-------+------+----+------+--------+------------+---------+-------------+----------+----------+------------+--------------+\n",
      "|1006032852|   Sexy|    Low|   4.6|   M|Summer|  o-neck|   sleevless|   empire|         null|   chiffon|   ruffles|      animal|             1|\n",
      "|1212192089| Casual|    Low|   0.0|   L|Summer|  o-neck|       Petal|  natural|   microfiber|      null|   ruffles|      animal|             0|\n",
      "|1190380701|vintage|   High|   0.0|   L|Automn|  o-neck|        full|  natural|     polyster|      null|      null|       print|             0|\n",
      "| 966005983|  Brief|Average|   4.6|   L|Spring|  o-neck|        full|  natural|         silk|   chiffon|embroidary|       print|             1|\n",
      "| 876339541|   cute|    Low|   4.5|   M|Summer|  o-neck|   butterfly|  natural|chiffonfabric|   chiffon|       bow|         dot|             0|\n",
      "+----------+-------+-------+------+----+------+--------+------------+---------+-------------+----------+----------+------------+--------------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# reading dataset to dataframe\n",
    "schema = StructType([\n",
    "    StructField(\"Dress_ID\", StringType(), True),\n",
    "    StructField(\"Style\", StringType(), True),\n",
    "    StructField(\"Price\", StringType(), True),\n",
    "    StructField(\"Rating\", FloatType(), True),\n",
    "    StructField(\"Size\", StringType(), True),\n",
    "    StructField(\"Season\", StringType(), True),\n",
    "    StructField(\"NeckLine\", StringType(), True),\n",
    "    StructField(\"SleeveLength\", StringType(), True),\n",
    "    StructField(\"waiseline\", StringType(), True),\n",
    "    StructField(\"Material\", StringType(), True),\n",
    "    StructField(\"FabricType\", StringType(), True),\n",
    "    StructField(\"Decoration\", StringType(), True),\n",
    "    StructField(\"Pattern Type\", StringType(), True),\n",
    "    StructField(\"Recommendation\", IntegerType(), True)])\n",
    "\n",
    "df = spark.read \\\n",
    "        .schema(schema) \\\n",
    "        .format(\"com.databricks.spark.csv\") \\\n",
    "        .option(\"header\", \"true\") \\\n",
    "        .load(\"Dresses_Attribute_Sales.csv\")\n",
    "\n",
    "df.show(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Các loại dữ liệu\n",
    "- Nomial\n",
    "- Numbers\n",
    "- Odinal\n",
    "- Ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+--------+-------------+------------+\n",
      "|  Style|NeckLine|     Material|Pattern Type|\n",
      "+-------+--------+-------------+------------+\n",
      "|   Sexy|  o-neck|         null|      animal|\n",
      "| Casual|  o-neck|   microfiber|      animal|\n",
      "|vintage|  o-neck|     polyster|       print|\n",
      "|  Brief|  o-neck|         silk|       print|\n",
      "|   cute|  o-neck|chiffonfabric|         dot|\n",
      "+-------+--------+-------------+------------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Nomial\n",
    "df_nomial = df[[\"Style\", \"NeckLine\", \"Material\", \"Pattern Type\"]]\n",
    "df_nomial.show(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----------+\n",
      "|  Dress_ID|\n",
      "+----------+\n",
      "|1006032852|\n",
      "|1212192089|\n",
      "|1190380701|\n",
      "| 966005983|\n",
      "| 876339541|\n",
      "+----------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Numbers\n",
    "df_numbers = df[[\"Dress_ID\"]]\n",
    "df_numbers.show(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----+\n",
      "|Size|\n",
      "+----+\n",
      "|   M|\n",
      "|   L|\n",
      "|   L|\n",
      "|   L|\n",
      "|   M|\n",
      "+----+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Ordinal\n",
    "df_ordinal = df[[\"Size\"]]\n",
    "df_ordinal.show(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------+\n",
      "|Rating|\n",
      "+------+\n",
      "|   4.6|\n",
      "|   0.0|\n",
      "|   0.0|\n",
      "|   4.6|\n",
      "|   4.5|\n",
      "+------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# ratio\n",
    "df_ratio = df[[\"Rating\"]]\n",
    "df_ratio.show(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trung tâm dữ liệu\n",
    "- Trung bình (mean)\n",
    "$$\\mu = \\bar{x} = \\frac{1}{n} \\sum_{i=1}^n x_i = \\frac{1}{n} (x_1 + ... + x_n)$$\n",
    "- Trung vị (median)\n",
    "- Mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+-----+--------+--------+------------+\n",
      "|summary|Style|NeckLine|Material|Pattern Type|\n",
      "+-------+-----+--------+--------+------------+\n",
      "|  count|  500|     499|     499|         499|\n",
      "|   mean| null|    null|    null|        null|\n",
      "| stddev| null|    null|    null|        null|\n",
      "|    min|Brief|    NULL| acrylic|      animal|\n",
      "|    max| work|  v-neck|    wool|     striped|\n",
      "+-------+-----+--------+--------+------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "df_nomial.describe().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+--------------------+\n",
      "|summary|            Dress_ID|\n",
      "+-------+--------------------+\n",
      "|  count|                 500|\n",
      "|   mean|      9.0554168105E8|\n",
      "| stddev|1.7361896065394258E8|\n",
      "|    min|          1000425584|\n",
      "|    max|           999081623|\n",
      "+-------+--------------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "df_numbers.describe().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+-----+\n",
      "|summary| Size|\n",
      "+-------+-----+\n",
      "|  count|  500|\n",
      "|   mean| null|\n",
      "| stddev| null|\n",
      "|    min|    L|\n",
      "|    max|small|\n",
      "+-------+-----+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "df_ordinal.describe().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------+------------------+\n",
      "|summary|            Rating|\n",
      "+-------+------------------+\n",
      "|  count|               500|\n",
      "|   mean|3.5285999937057495|\n",
      "| stddev|  2.00536405618619|\n",
      "|    min|               0.0|\n",
      "|    max|               5.0|\n",
      "+-------+------------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "df_ratio.describe().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean rating: 3.52859999371\n"
     ]
    }
   ],
   "source": [
    "mean_rating = df_ratio.agg(F.mean(df_ratio.Rating)).first()[0]\n",
    "print \"Mean rating:\", mean_rating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median rating: 4.59999990463\n"
     ]
    }
   ],
   "source": [
    "sqlContext.registerDataFrameAsTable(df_ratio, \"df_ratio\")\n",
    "\n",
    "median_rating = sqlContext.sql(\"\"\"\n",
    "    SELECT percentile(Rating, 0.5) AS median_rating \n",
    "    FROM df_ratio\n",
    "\"\"\").first()[\"median_rating\"]\n",
    "\n",
    "print \"Median rating:\", median_rating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mode rating: 0.0\n"
     ]
    }
   ],
   "source": [
    "counts = df_ratio.groupBy(\"Rating\").count()\n",
    "\n",
    "mode_rating = counts.join(\n",
    "        counts.agg(F.max('count').alias('count')),\n",
    "        on='count'\n",
    "    ).limit(1).select(\"Rating\").first()[\"Rating\"]\n",
    "\n",
    "print \"Mode rating:\", mode_rating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hongong/virtualenv/trustingsocial/lib/python2.7/site-packages/matplotlib/axes/_axes.py:545: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n",
      "  warnings.warn(\"No labelled objects found. \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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gJ0mSJEk9Z/CTJEmSpJ4z+EmSJElSzxn8JEmSJKnnDH6SJEmS1HMGP0mSJEnq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\nM/hJkiRJUs8Z/CRJkiSp5/4/ZSB5a9HkxV8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e4306d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize price column\n",
    "fig, ax = plt.subplots(figsize=(15, 5))\n",
    "ax.axvline(mean_rating, color='red', linewidth=5)\n",
    "ax.axvline(median_rating, color='green', linewidth=5)\n",
    "ax.axvline(mode_rating, color='blue', linewidth=5)\n",
    "\n",
    "# Add arrows annotating the means:\n",
    "def add_arrow(label, val, align=\"left\"):\n",
    "    ax.annotate(label + ': {:0.2f}'.format(val), xy=(val, 1), xytext=(15, 15),\n",
    "            xycoords=('data', 'axes fraction'), textcoords='offset points',\n",
    "            horizontalalignment=align, verticalalignment='center',\n",
    "            arrowprops=dict(arrowstyle='-|>', fc='black', shrinkA=0, shrinkB=0,\n",
    "                            connectionstyle='angle,angleA=0,angleB=90,rad=10'),\n",
    "            )\n",
    "\n",
    "add_arrow(\"Mean\", mean_rating)\n",
    "add_arrow(\"Median\", median_rating)\n",
    "add_arrow(\"Mode\", mode_rating)\n",
    "ax.legend(loc='upper left')\n",
    "ax.margins(0.05)\n",
    "\n",
    "bins, hist = df_ratio.select(\"Rating\").rdd.flatMap(lambda x: x).histogram(70)\n",
    "hist = np.asarray(hist)\n",
    "bins = np.asarray(bins)\n",
    "width = 0.7 * (bins[1] - bins[0])\n",
    "center = (bins[:-1] + bins[1:]) / 2\n",
    "plt.bar(center, hist, align='center', width=width)\n",
    "plt.title(\"Rating Histogram\")\n",
    "plt.xlabel(\"Rating\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Biến đổi của dữ liệu \n",
    "- Khoảng đoạn (range)\n",
    "$$range = maxValue - minValue$$\n",
    "\n",
    "- Phương sai (variance)\n",
    "$$\\sigma^2 = \\frac{\\sum_{i=1}^n (x_i - \\mu)}{n}$$\n",
    "\n",
    "- Độ lệch chuẩn (standard deviation)\n",
    "$$\\sigma = \\sqrt{\\frac{\\sum_{i=1}^n (x_i - \\mu)}{n}}$$\n",
    "\n",
    "- Z-score: biến đổi từ sample mean để thực hiện Z-test\n",
    "    * Shift trung bình mẫu về 0 bằng $X - \\mu$\n",
    "    * Nén độ lệch chuẩn của mẫu ban đầu lại bằng cách chia cho $\\sigma$\n",
    "$$Z = \\frac{X - \\mu}{\\sigma}$$\n",
    "\n",
    "- Phân vị (percentile)\n",
    "$$percentile \\ of \\ x = \\frac{No. value \\ below \\ x}{n} * 100\\\\$$\n",
    "$$quartiles = \\frac{percentile * n}{100}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min rating: 0.0\n",
      "Max rating: 5.0\n",
      "Rating range: 5.0\n"
     ]
    }
   ],
   "source": [
    "# range of rating\n",
    "min_rating = df_ratio.agg(F.min(df_ratio.Rating)).first()[0]\n",
    "max_rating = df_ratio.agg(F.max(df_ratio.Rating)).first()[0]\n",
    "range_rating = max_rating - min_rating\n",
    "print \"Min rating:\", min_rating\n",
    "print \"Max rating:\", max_rating\n",
    "print \"Rating range:\", range_rating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rating variance: 4.02148499784\n"
     ]
    }
   ],
   "source": [
    "# variance of rating\n",
    "var_rating = df_ratio.agg(F.variance(df_ratio.Rating)).first()[0]\n",
    "print \"Rating variance:\", var_rating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rating standard deviation: 2.00536405619\n"
     ]
    }
   ],
   "source": [
    "# standard deviation of rating\n",
    "std_rating = df_ratio.agg(F.stddev(df_ratio.Rating)).first()[0]\n",
    "print \"Rating standard deviation:\", std_rating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Z-score of rating:\n",
      "+-------------------+\n",
      "|             Rating|\n",
      "+-------------------+\n",
      "|  2.840419152789433|\n",
      "|-1.7595807518431354|\n",
      "|-1.7595807518431354|\n",
      "|  2.840419152789433|\n",
      "| 2.7404192481568646|\n",
      "+-------------------+\n",
      "only showing top 5 rows\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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AAQAAoAAKOAAAABRAAQcAAIACKOAAAABQAAUcAAAACqCAAwAAQAEUcAAAACiA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\nfzYvcwDmPlEGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e65c290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# z-score of rating\n",
    "df_z_score_rating = sqlContext.sql(\"SELECT (Rating - \" + \\\n",
    "                                   str(mean_rating) + \" / \" + str(std_rating) + \\\n",
    "                                   \") as Rating FROM df_ratio\")               \n",
    "\n",
    "print \"\\nZ-score of rating:\"\n",
    "df_z_score_rating.show(5)\n",
    "\n",
    "bins, hist = df_z_score_rating.select(\"Rating\").rdd.flatMap(lambda x: x).histogram(70)\n",
    "hist = np.asarray(hist)\n",
    "bins = np.asarray(bins)\n",
    "width = 0.7 * (bins[1] - bins[0])\n",
    "center = (bins[:-1] + bins[1:]) / 2\n",
    "\n",
    "# plotting\n",
    "fig = plt.figure(figsize=(15, 5), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.bar(center, hist, align='center', width=width)\n",
    "plt.title(\"Z score distribution\")\n",
    "plt.xlabel(\"Rating\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Xác suất\n",
    "- Xác suất (probability)\n",
    "$$probability = \\frac{event(s)}{outcome(s)}$$\n",
    "\n",
    "- Phép đếm hoán vị (permutation)\n",
    "$$P(n, r) = \\frac{n!}{(n - r)!}\\\\$$\n",
    "$$n: distinct\\ object\\ to\\ choose\\ from$$\n",
    "$$r: spaces\\ to\\ fill.$$\n",
    "\n",
    "- Phép đếm tổ hợp (combination)\n",
    "$$C(n, r) = \\frac{n!}{r!(n - r)!}$$\n",
    "\n",
    "- Xác suất có điều kiện (conditional probability)\n",
    "$$P(B|A) = \\frac{P(A \\cap B)}{P(A)}$$\n",
    "\n",
    "- Biến độc lập và biến phụ thuộc (independent/dependent variable)\n",
    "    - Independent variable: \n",
    "        * Dress_ID\n",
    "        * Style\n",
    "        * Price\n",
    "        * Rating\n",
    "        * Size\n",
    "        * Season\n",
    "        * NeckLine\n",
    "        * SleeveLength\n",
    "        * waiseline\n",
    "        * Material\n",
    "        * FabricType\n",
    "        * Decoration\n",
    "        * Pattern Type\n",
    "    - Dependent variable: Recommendation\n",
    "\n",
    "- Bayes\n",
    "$$P(A|B) = \\frac{P(B|A) P(A)}{P(B)}\\\\$$\n",
    "$$Posterior = \\frac{Likelihood * Prior}{Evidence}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(Season:summer) 31.8\n",
      "P(Style:sexy and Season:summer) 4.8\n",
      "P(Style:sexy|Season:summer) 15.0943396226\n"
     ]
    }
   ],
   "source": [
    "# Conditional probability\n",
    "# P(Style:sexy|Season:summer) = P(Style:sexy and Season:summer) / P(Season:summer)\n",
    "num_items = df.select(\"Rating\").count()\n",
    "df_summer = df.select(\"Season\").where(df[\"Season\"] == \"Summer\")\n",
    "p_summer = df_summer.count() * 100.0 / num_items\n",
    "\n",
    "df_sexy_summer = df.select(df.Style, df.Season).where(\"Style = 'Sexy' and Season = 'Summer'\")\n",
    "p_sexy_summer = df_sexy_summer.count() * 100.0 / num_items\n",
    "\n",
    "p_sexy_given_summer = p_sexy_summer * 100 / p_summer\n",
    "\n",
    "print \"P(Season:summer)\", p_summer\n",
    "print \"P(Style:sexy and Season:summer)\", p_sexy_summer\n",
    "print \"P(Style:sexy|Season:summer)\", p_sexy_given_summer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(Style:sexy) 13.8\n",
      "P(Season:summer) 31.8\n",
      "P(Season:summer|Style:sexy) 34.7826086957\n",
      "P(Style:sexy|Season:summer) Bayes: 15.0943396226\n"
     ]
    }
   ],
   "source": [
    "# Bayes\n",
    "# P(Style:sexy|Season:summer) = P(Season:summer|Style:sexy) * P(Style:sexy) / P(Season:summer)\n",
    "num_items = df.select(\"Rating\").count()\n",
    "df_style = df.select(df.Style).where(\"Style = 'Sexy'\")\n",
    "p_sexy = df_style.count() * 100.0 / num_items\n",
    "\n",
    "p_summer_given_sexy = p_sexy_summer * 100 / p_sexy\n",
    "\n",
    "p_sexy_given_summer_bayes = p_summer_given_sexy * p_sexy / p_summer\n",
    "\n",
    "print \"P(Style:sexy)\", p_sexy\n",
    "print \"P(Season:summer)\", p_summer\n",
    "print \"P(Season:summer|Style:sexy)\", p_summer_given_sexy\n",
    "print \"P(Style:sexy|Season:summer) Bayes:\", p_sexy_given_summer_bayes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Central limit theorem\n",
    "- Dịch thành: Định lý giới hạn trung tâm.\n",
    "- Cho quần thể có phân bố bất kỳ.\n",
    "- Ta thực hiện lấy mẫu nhiều lần trên quần thể cho trước với số lượng xác định.\n",
    "- Mỗi lần lấy mẫu ta đi tính trung bình mẫu\n",
    "- Tổng hợp các trung bình mẫu này lại thành histogram.\n",
    "- Quan sát phân phối của trung bình mẫu của các mẫu ngẫu nhiên, ta thấy đây gần giống với phân phối chuẩn dù cho quần thể ban đầu có phân bố bất kỳ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulating Central limit theorem\n",
    "num_sample = 30.0\n",
    "num_loop = 1000\n",
    "num_items = df.select(\"Rating\").count()\n",
    "samp_mean_ls = []\n",
    "\n",
    "for i in range(0, num_loop):\n",
    "    df_rating_sample = df.select(\"Rating\").sample(False, num_sample / num_items)\n",
    "    sum_of_sample = df_rating_sample.agg(F.sum(df_rating_sample.Rating)).first()[0]\n",
    "\n",
    "    x_bar = sum_of_sample * 100 / num_sample\n",
    "    samp_mean_ls.append(x_bar)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAAAAAJsQwgEAAAAAsAkhHAAAAAAAmxDCAQAAAACwCSEcAAAAAACbOP1dAAAA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10efea910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ploting population\n",
    "fig = plt.figure(figsize=(15, 5), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.subplot(1, 2, 1)\n",
    "bins, hist = df_ratio.select(\"Rating\").rdd.flatMap(lambda x: x).histogram(70)\n",
    "hist = np.asarray(hist)\n",
    "bins = np.asarray(bins)\n",
    "width = 0.7 * (bins[1] - bins[0])\n",
    "center = (bins[:-1] + bins[1:]) / 2\n",
    "\n",
    "plt.bar(center, hist, align='center', width=width)\n",
    "plt.title(\"Population distribution: Rating\")\n",
    "plt.xlabel(\"Rating\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "\n",
    "# ploting sampling\n",
    "plt.subplot(1, 2, 2)\n",
    "hist, bins = np.histogram(samp_mean_ls)\n",
    "width = 0.7 * (bins[1] - bins[0])\n",
    "center = (bins[:-1] + bins[1:]) / 2\n",
    "plt.bar(center, hist, align='center', width=width)\n",
    "plt.title(\"Sampling distribution of mean: Rating\")\n",
    "plt.xlabel(\"Sample mean\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}