02-Data-and-Sampling-Distributions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <div class=\"alert alert-info\" style=\"text-align: center;\" markdown=\"1\">Data and Sampling Distributions</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Sampling Distributions`\n",
    "\n",
    "- A sampling distribution is a distribution of a statistic obtained through a large number of samples drawn from a specific population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>status</th>\n",
       "      <th>loan_amnt</th>\n",
       "      <th>term</th>\n",
       "      <th>annual_inc</th>\n",
       "      <th>dti</th>\n",
       "      <th>payment_inc_ratio</th>\n",
       "      <th>revol_bal</th>\n",
       "      <th>revol_util</th>\n",
       "      <th>purpose</th>\n",
       "      <th>...</th>\n",
       "      <th>delinq_2yrs_zero</th>\n",
       "      <th>pub_rec_zero</th>\n",
       "      <th>open_acc</th>\n",
       "      <th>grade</th>\n",
       "      <th>outcome</th>\n",
       "      <th>emp_length</th>\n",
       "      <th>purpose_</th>\n",
       "      <th>home_</th>\n",
       "      <th>emp_len_</th>\n",
       "      <th>borrower_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Charged Off</td>\n",
       "      <td>2500</td>\n",
       "      <td>60 months</td>\n",
       "      <td>30000</td>\n",
       "      <td>1.00</td>\n",
       "      <td>2.39320</td>\n",
       "      <td>1687</td>\n",
       "      <td>9.4</td>\n",
       "      <td>car</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>4.8</td>\n",
       "      <td>default</td>\n",
       "      <td>1</td>\n",
       "      <td>major_purchase</td>\n",
       "      <td>RENT</td>\n",
       "      <td>&gt; 1 Year</td>\n",
       "      <td>0.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>Charged Off</td>\n",
       "      <td>5600</td>\n",
       "      <td>60 months</td>\n",
       "      <td>40000</td>\n",
       "      <td>5.55</td>\n",
       "      <td>4.57170</td>\n",
       "      <td>5210</td>\n",
       "      <td>32.6</td>\n",
       "      <td>small_business</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>1.4</td>\n",
       "      <td>default</td>\n",
       "      <td>5</td>\n",
       "      <td>small_business</td>\n",
       "      <td>OWN</td>\n",
       "      <td>&gt; 1 Year</td>\n",
       "      <td>0.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Charged Off</td>\n",
       "      <td>5375</td>\n",
       "      <td>60 months</td>\n",
       "      <td>15000</td>\n",
       "      <td>18.08</td>\n",
       "      <td>9.71600</td>\n",
       "      <td>9279</td>\n",
       "      <td>36.5</td>\n",
       "      <td>other</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>6.0</td>\n",
       "      <td>default</td>\n",
       "      <td>1</td>\n",
       "      <td>other</td>\n",
       "      <td>RENT</td>\n",
       "      <td>&gt; 1 Year</td>\n",
       "      <td>0.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Charged Off</td>\n",
       "      <td>9000</td>\n",
       "      <td>36 months</td>\n",
       "      <td>30000</td>\n",
       "      <td>10.08</td>\n",
       "      <td>12.21520</td>\n",
       "      <td>10452</td>\n",
       "      <td>91.7</td>\n",
       "      <td>debt_consolidation</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4.2</td>\n",
       "      <td>default</td>\n",
       "      <td>1</td>\n",
       "      <td>debt_consolidation</td>\n",
       "      <td>RENT</td>\n",
       "      <td>&gt; 1 Year</td>\n",
       "      <td>0.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>Charged Off</td>\n",
       "      <td>10000</td>\n",
       "      <td>36 months</td>\n",
       "      <td>100000</td>\n",
       "      <td>7.06</td>\n",
       "      <td>3.90888</td>\n",
       "      <td>11997</td>\n",
       "      <td>55.5</td>\n",
       "      <td>other</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>14</td>\n",
       "      <td>5.4</td>\n",
       "      <td>default</td>\n",
       "      <td>4</td>\n",
       "      <td>other</td>\n",
       "      <td>RENT</td>\n",
       "      <td>&gt; 1 Year</td>\n",
       "      <td>0.55</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0       status  loan_amnt       term  annual_inc    dti  \\\n",
       "0           1  Charged Off       2500  60 months       30000   1.00   \n",
       "1           2  Charged Off       5600  60 months       40000   5.55   \n",
       "2           3  Charged Off       5375  60 months       15000  18.08   \n",
       "3           4  Charged Off       9000  36 months       30000  10.08   \n",
       "4           5  Charged Off      10000  36 months      100000   7.06   \n",
       "\n",
       "   payment_inc_ratio  revol_bal  revol_util             purpose  ...  \\\n",
       "0            2.39320       1687         9.4                 car  ...   \n",
       "1            4.57170       5210        32.6      small_business  ...   \n",
       "2            9.71600       9279        36.5               other  ...   \n",
       "3           12.21520      10452        91.7  debt_consolidation  ...   \n",
       "4            3.90888      11997        55.5               other  ...   \n",
       "\n",
       "  delinq_2yrs_zero  pub_rec_zero  open_acc  grade  outcome emp_length  \\\n",
       "0                1             1         3    4.8  default          1   \n",
       "1                1             1        11    1.4  default          5   \n",
       "2                1             1         2    6.0  default          1   \n",
       "3                1             1         4    4.2  default          1   \n",
       "4                1             1        14    5.4  default          4   \n",
       "\n",
       "             purpose_ home_   emp_len_ borrower_score  \n",
       "0      major_purchase  RENT   > 1 Year           0.65  \n",
       "1      small_business   OWN   > 1 Year           0.80  \n",
       "2               other  RENT   > 1 Year           0.60  \n",
       "3  debt_consolidation  RENT   > 1 Year           0.50  \n",
       "4               other  RENT   > 1 Year           0.55  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_loan = pd.read_csv(\"data/loan_data.csv.gz\")\n",
    "df_loan.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_1000 = pd.DataFrame({\n",
    "    'income': df_loan[\"annual_inc\"].sample(1000),\n",
    "    'type': 'Data',\n",
    "})\n",
    "sample_05 = pd.DataFrame({\n",
    "    'income': [df_loan[\"annual_inc\"].sample(5).mean() for _ in range(1000)],\n",
    "    'type': 'Sample 5',\n",
    "})\n",
    "sample_20 = pd.DataFrame({\n",
    "    'income': [df_loan[\"annual_inc\"].sample(20).mean() for _ in range(1000)],\n",
    "    'type': 'Sample 20',\n",
    "})\n",
    "\n",
    "sample = pd.concat([sample_1000, sample_05, sample_20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Data         1000\n",
       "Sample 5     1000\n",
       "Sample 20    1000\n",
       "Name: type, dtype: int64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample.type.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x900 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.FacetGrid(sample, col='type', col_wrap=1, aspect=2).map(sns.histplot, 'income', bins=40).set_titles('{col_name}').set_axis_labels('Income', 'Count')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Central Limit Theorem\n",
    "\n",
    "- The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normally distributed, regardless of the shape of the population distribution. - Provided that the sample size is sufficiently large."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard Error\n",
    "\n",
    "- The standard error is the standard deviation of the sampling distribution of a statistic. It is a measure of the variability of the sample statistic.\n",
    "\n",
    "$$SE = \\frac{s}{\\sqrt{n}}$$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $s$ = Standard deviation of the population\n",
    "- $n$ = sample size\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `The Bootstrap`\n",
    "\n",
    "- The bootstrap is a resampling technique used to estimate statistics on a population by sampling with replacement.\n",
    "\n",
    "Algorithm:\n",
    "\n",
    "1. Draw a sample of size n with replacement from the original sample.\n",
    "2. Calculate the statistic of interest.\n",
    "3. Repeat steps 1 and 2 a large number of times.\n",
    "4. Calculate the standard deviation of the bootstrapped statistics.\n",
    "5. Produce a histogram or boxplot of the bootstrapped statistics.\n",
    "6. Calculate the confidence interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrao Statistics:\n",
      "Original: 60000.0\n",
      "bias: -275.1924999999974\n",
      "std. error: 403.8757424122656\n"
     ]
    }
   ],
   "source": [
    "from sklearn.utils import resample\n",
    "\n",
    "results = []\n",
    "\n",
    "for _ in range(1000):\n",
    "    sample = resample(df_loan[\"annual_inc\"])\n",
    "    results.append(sample.median())\n",
    "\n",
    "results = pd.Series(results)\n",
    "\n",
    "print(\"Bootstrao Statistics:\")\n",
    "print(f\"Original: {df_loan['annual_inc'].median()}\")\n",
    "print(f\"bias: {results.mean() - df_loan['annual_inc'].median()}\")\n",
    "print(f\"std. error: {results.std()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Confidence Intervals`\n",
    "\n",
    "- A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter.\n",
    "\n",
    "Algorithm:\n",
    "\n",
    "1. Draw random samples of size n with replacement from the original data.\n",
    "2. Calculate the statistic of interest.\n",
    "3. Repeat steps 1 and 2 a large number of times.\n",
    "4. For an x% confidence interval, trim [(100-x)/2]% from resampled results from any side of the distribution.\n",
    "5. The trimmed values are the lower and upper bounds of the confidence interval.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Normal Distribution`\n",
    "\n",
    "- A normal distribution is a continuous probability distribution that is symmetric about the mean.\n",
    "\n",
    "### Properties of Normal Distribution\n",
    "\n",
    "- In normal distribution, 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.\n",
    "\n",
    "\n",
    "### Standard Normal Distribution\n",
    "\n",
    "- A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.\n",
    "\n",
    "### Z-Score\n",
    "\n",
    "- The Z-score is the number of standard deviations a data point is from the mean.\n",
    "\n",
    "$Z = \\frac{x - \\mu}{\\sigma}$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $x$ = data point\n",
    "- $\\mu$ = mean\n",
    "- $\\sigma$ = standard deviation\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard Normal and QQ Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm, probplot\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "norm_sample = norm.rvs(size=100)\n",
    "probplot(norm_sample, plot=ax) \n",
    "plt.ylabel(\"Z-Scores\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Long-Tailed Distributions\n",
    "\n",
    "- A long-tailed distribution is a distribution with a tail that extends further than a normal distribution.\n",
    "\n",
    "### Skewness\n",
    "\n",
    "- Skewness is a measure of the asymmetry of a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "sp500_px = pd.read_csv(\"data/sp500_data.csv.gz\", index_col=0)\n",
    "nflx = sp500_px[\"NFLX\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nflx = np.diff(np.log(nflx[nflx>0]))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "probplot(nflx, plot=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The points are far below for the left-skewed distribution and far above for the right-skewed distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Long-Tailed Distributions with KDE Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(data=nflx)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Student's t-Distribution`\n",
    "\n",
    "- The t-distribution is a continuous probability distribution that is symmetric and bell-shaped, like the normal distribution, but has heavier tails.\n",
    "\n",
    "#### Degrees of Freedom\n",
    "\n",
    "- A parameter that allows the t-distribution to adjust to different sample sizes.\n",
    "\n",
    "$t = \\frac{\\bar{x} - \\mu}{\\frac{s}{\\sqrt{n}}}$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $\\bar{x}$ = sample mean\n",
    "- $\\mu$ = population mean\n",
    "- $s$ = sample standard deviation\n",
    "- $n$ = sample size\n",
    "\n",
    "\n",
    "- A 90% confidence interval around sample mean is given by:\n",
    "\n",
    "$\\bar{x} \\pm t_{n-1} \\times (0.05) \\times \\frac{s}{\\sqrt{n}}$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $t_{n-1}(0.05)$ is the value of t-statistic with degrees of freedom n-1, which chops off 5% from each tail of the distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Binoial Distribution`\n",
    "\n",
    "- The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of Bernoulli trials.\n",
    "\n",
    "Formula:\n",
    "\n",
    "$P(X = k) = \\binom{n}{k} \\times p^k \\times (1-p)^{n-k}$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $n$ = number of trials\n",
    "- $k$ = number of successes\n",
    "- $p$ = probability of success\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.07178753716621049, 0.017587946605721567)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "stats.binom.pmf(1, n=200, p=0.02), stats.binom.cdf(0, n=200, p=0.02)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Chi-Square Distribution`\n",
    "\n",
    "- The statistic that measures the extent to which observed counts deviate from expected counts.\n",
    "\n",
    "Formula:\n",
    "\n",
    "$\\chi^2 = \\sum \\frac{(O - E)^2}{E}$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $O$ = observed frequency\n",
    "- $E$ = expected frequency\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `F-Distribution`\n",
    "\n",
    "- The F-distribution is a continuous probability distribution that is used in the analysis of variance (ANOVA).\n",
    "- Its is the ratio of the variablity between groups means to the variability within group means.\n",
    "\n",
    "Formula:\n",
    "\n",
    "$F = \\frac{SSE_{between}}{SSE_{within}}$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $SSE_{between}$ = Sum of squares of the differences between group means and overall mean.\n",
    "- $SSE_{within}$ = Sum of squares of the differences between individual observations and their group mean.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `Poisson and Related Distributions`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson Distribution\n",
    "\n",
    "- The Poisson distribution is a discrete probability distribution that describes the number of events in a fixed interval of time or space.\n",
    "\n",
    "Formula:\n",
    "\n",
    "$P(X = k) = \\frac{e^{-\\lambda} \\times \\lambda^k}{k!}$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $k$ = number of events\n",
    "- $\\lambda$ = average rate of events\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 3, 2, 2, 3, 0, 2, 1, 4, 1, 3, 1, 0, 1, 2, 3, 1, 2, 2, 1, 4, 0,\n",
       "       1, 1, 1, 2, 2, 2, 0, 4, 3, 3, 3, 3, 3, 1, 3, 2, 2, 2, 1, 1, 3, 1,\n",
       "       1, 2, 0, 2, 1, 3, 3, 1, 1, 5, 2, 1, 1, 4, 2, 1, 2, 0, 4, 4, 3, 2,\n",
       "       3, 2, 1, 2, 1, 2, 0, 1, 0, 1, 4, 3, 2, 2, 0, 2, 0, 3, 0, 1, 1, 1,\n",
       "       2, 2, 6, 4, 3, 1, 3, 3, 3, 1, 0, 0])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.poisson.rvs(2, size=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exponential Distribution\n",
    "\n",
    "- The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process.\n",
    "\n",
    "Formula:\n",
    "\n",
    "$P(X = x) = \\lambda \\times e^{-\\lambda x}$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $x$ = time between events\n",
    "- $\\lambda$ = average rate of events\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.37925813, 0.72314053, 0.76597617, 1.20279656, 0.33205738,\n",
       "       1.19353936, 0.97561181, 0.29756682, 0.22327315, 0.24990069,\n",
       "       0.19968025, 0.32725022, 0.02926009, 0.08310847, 0.16781418,\n",
       "       0.27944471, 0.28901256, 0.18201733, 0.04513125, 1.37943879,\n",
       "       0.67092794, 0.26836829, 2.10045254, 0.10961605, 0.58560722,\n",
       "       0.02753224, 0.09322598, 0.13212395, 0.18797538, 0.12360647,\n",
       "       0.36359732, 0.55029655, 0.22149491, 0.04733365, 0.06217855,\n",
       "       0.61984215, 0.08566009, 0.05183339, 0.03854244, 0.26901987,\n",
       "       0.14752108, 0.08760391, 0.9782585 , 1.05551929, 0.50389719,\n",
       "       0.08704713, 0.02833777, 0.55763417, 0.07578084, 0.32347715,\n",
       "       0.19696648, 1.35054494, 0.22140305, 1.17359075, 0.50838454,\n",
       "       0.1533625 , 0.20173992, 0.54676261, 0.5888478 , 0.02584672,\n",
       "       0.00744257, 0.39842171, 0.04390362, 0.29669985, 0.2480477 ,\n",
       "       0.63700568, 0.7664952 , 0.09877835, 0.04285784, 0.32867346,\n",
       "       0.17112232, 1.04488082, 0.14007418, 1.85916154, 0.22374526,\n",
       "       0.18337499, 0.76025265, 0.10860738, 0.33951738, 0.5894064 ,\n",
       "       0.29688765, 1.12847521, 1.26198084, 0.06197635, 1.04856038,\n",
       "       0.55731852, 0.74826679, 0.49849738, 1.31432747, 0.046141  ,\n",
       "       0.35209261, 0.49563467, 0.39924018, 0.58868434, 0.10622303,\n",
       "       0.17966214, 1.1656299 , 0.17114426, 0.11740663, 0.59308516])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.expon.rvs(scale=1/2, size=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating the Failure Rate\n",
    "\n",
    "- The failure rate is the number of failures that occur in a given time period."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weibull Distribution\n",
    "\n",
    "- The Weibull distribution is a continuous probability distribution that is used to model the life of products.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2736.874062  ,  1961.11226312,  6110.5927517 ,  1606.97590914,\n",
       "        2100.6306701 , 13970.01073472,  6315.75171748,  1051.73116558,\n",
       "        3262.5088588 ,   686.18575601,  2449.39406312,  4828.27929878,\n",
       "         892.30733816,  8083.84287594,  5708.07548507,  2608.86560542,\n",
       "        3844.73202614,  3871.03163031,  5940.50254441,  6322.31746852,\n",
       "        1667.76871948,  3011.62315674,  2088.55326696,  5134.37809927,\n",
       "        1772.58064993,  5501.5256637 ,  1150.97521631,  2915.80576198,\n",
       "        7825.0962581 ,  4390.42207876,  1836.74360382,  7622.05581762,\n",
       "         650.19191941,   311.99693697,  4658.6276131 ,  2391.25830532,\n",
       "        4706.11412741,  2213.18910024,  1257.60138598,  2720.18708784,\n",
       "        1930.07859299,  2319.73640622,  7243.70404421,   278.10874919,\n",
       "        3262.99084271,  8003.83657259,  5064.13355178,  3298.28454718,\n",
       "        2804.02980794,  4797.22204554,  5257.01111064,  1514.5680073 ,\n",
       "        7904.5750905 ,   894.76052475, 11286.29949247,  1620.34943827,\n",
       "        4567.20190567,  7259.32995353,  8549.75309225,  6345.53491618,\n",
       "        8077.65274446,  4097.0748846 ,  3265.64715535,  3142.09017819,\n",
       "        8167.41431   ,  1554.29193694,  2116.12360606,  4588.09429021,\n",
       "        4609.72785189,  5447.74964094,  3376.94735461,  9357.62208155,\n",
       "        7060.82279858,  1444.78389606,  9775.88578041,  1176.94170301,\n",
       "        3623.90781793,  1697.52538091,  4846.04190221,  2543.06323049,\n",
       "        1168.60609954,  4362.13130752,  2816.15131262,  3249.55145779,\n",
       "        3549.42088179,  4900.8602423 ,   733.84962505,  1159.37384336,\n",
       "        5026.92660963,  3237.55415952,  2663.06661263,  8567.15536644,\n",
       "        2698.43112829,  4263.00360375,  6038.14236201,  1973.87169051,\n",
       "        4957.10156962,  3358.93977237,  7637.11705811,   561.70963093])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.weibull_min.rvs(1.5, scale=5000, size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}