/Two sample testing gauss vs laplace.ipynb

## Two sample testing gauss vs laplace.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
      "  warnings.warn(self.msg_depr % (key, alt_key))\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm, laplace\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n=500\n",
    "mu=2.0\n",
    "sigma2=2\n",
    "b=np.sqrt(2)\n",
    "X=norm.rvs(size=n, loc=mu, scale=sigma2)\n",
    "Y=laplace.rvs(size=n, loc=mu, scale=b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample means: 2.04 vs 1.97\n",
      "Samples variances: 4.47 vs 3.32\n"
     ]
    }
   ],
   "source": [
    "print \"Sample means: %.2f vs %.2f\" % (np.mean(X), np.mean(Y))\n",
    "print \"Samples variances: %.2f vs %.2f\" % (np.var(X), np.var(Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.savetxt(\"two_sample_test_gaussian.dat\",X.reshape(n/2,2))\n",
    "np.savetxt(\"two_sample_test_laplace.dat\", Y.reshape(n/2,2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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9ED7N2/wCMD6ajm/U234ijUgBQFpRX/X/h+KafV6ZS0ZW9PC+Hzfh5rk4wRs+Qs8BpCkp\nAEgr6isAHOutrxnoh+eSkXXAxUDhbkIBQJqSAoC0ot1wQzhsMIhbOJHdFvg08M9cMvLfQX7HdcAy\n4Jv5dcNf9rYpAEhTUQCQlhJNx8cAOwIPZ2KpzpK3j/HW1w32e7xnAb8GNupYNHVnb7MCgDQVBQBp\nNbvhegBvUP3j9d79GrAS+FOFvusqYF3nW5se7r1WAJCmogAgrWYfb/3Pku2fAbYGZg2g6WePvH4B\nv6OrfUq+q+0tYLtKfK5IrSgASKvZBzdJ+H0l27/urQdd/VPilwD5NaNCwKRoOj60wp8vUjUKANIy\nvDmA9wCezMRSbxS2hxPZ8cAXcL2C/1PJ78wlI48Df+9atdFGuL4H21by80WqSQFAWskMXAetf5Rs\nPwoYBlzX36BvA/TL/JpRhZ93qMLni1SFAoC0kkL9f2kAOBZYj+vAVQ235deNXAaQ7xi2a5W+Q6Ti\nFACklezrrd97ABxOZKcDHwVy3kPbisslI535rrYbALpWjz6wGt8hUg0KANISoun4MNxk7k9nYqnX\nit4q9Pyt9MPfDYSGrP+5+yH/0XAiq6lWpSkoAEir2BM3NMO9hQ3hRHYEbtavpcCd1fzyW886aVl+\n/dCVbcNXD8c9cBZpeL6uVIwxM4FLcQHjWmvtxSXvG+B63CxM37PW/rzovQXACqAL6LDWzqhIzkU2\ndJC3/kvRtkNwwz5fmUtG1lc9B6GuJ0PDOj7OkI5vU7nOZiJV0+8dgDGmDbgc2A+YBhxpjJlakmw5\ncArwsx4+ogvY11q7q07+UkUHAe8Cfy/aVqj+ub4WGQgN6XwMIDR89V7hRFYPg6Xh+akCmgHMt9Yu\ntNZ2ALOASHECa+3r1tqHcS0tSoV8fo/IgETT8SnAVOCeTCy1BiCcyE7C9f69P5eMPFejrDwH0DZi\nFbgLIpGG5ufEvBVu7POCxd42v/LA3caYucaY48rJnIhPhZY3uaJtX8NdfFT14W+J5wBCo1YuB44K\nJ7Kb1vC7RcpWiyvzvay104EDgJOMMXv73C+vhUKnpXrnoRGWXsthp82nXgpw5cEXXQPku7ry+U03\nHnnuyOFDyPz4wOtqlcfLDjz/dgCz3YjxwPCj99/x1VqXRQAXlcWGZVEWPwFgCbBN0esJ3jZfrLVL\nvfVrwC24KiU/QloIqSz6LodoOj7uyWXPdgAPbzJyXAgIRU6f/bnX3lzN6rWd144c3l6zPH7rLz8Y\nCnQ8/+68h4GVN90xb0k4kR2mY6L2x0VAl7L5CQBzgSnGmInGmGHAEcDsPtK/lxFjzChjzBjv59HA\n54GnBpJRkV4cAgwFbi3aVpO2/6UysdR64L+hUH57yF+Pqyo9pJZ5EClHv81ArbWdxpiTgbvobgY6\nzxhzApC31l5tjNkcN/76WKDLGHMq8GFgU+AWY0ze+67fWWvvqtYvI4F0pLf+PUA4kd0YN+/vs8C/\n65Cfp4Ed27d48Y/rX5n8LeBbQKYO+RDpl69+ANbaOwFTsu2qop+X4cZaL/UOrhu+SMVF0/HNgc8C\nczKxVGFe3i8Dw6newG/9eQZg6DbPjVr/yuTbgQPCieweuWRkTh3yItInNc+UZhbFHcOFq/8QEAc6\ngBvqlKenvfWH6e4Xc2ad8iLSJwUAaWZH4ToaFqpYPombD/hP1Rr4zYdnvPU03Kikc4BIOJH9SJ3y\nI9IrBQBpStF0fDJu8pd7MrHUMm9z3FtfUZ9cAa4vQCfwYa8K6iJv+xn1y5JIzxQApFkVHv7+ASCc\nyG4BHIZrZfZAvTKViaXWAfOBadF0PATchqsWOjKcyG5br3yJ9EQBQJqOd2I9CliL61sCbs7fduCK\nOj38LfYMsBGwZS4Z6QJ+gpsu8rS65kqkhAKANKOdcA9Zb8vEUivCiewQ4Hhcq7Pf1jVnTvGDYHDj\nZy0Avu7dqYg0BAUAaUZHeevfe+sDcL3Vf5tLRlbWJ0sbKH4QjDcU9U9xzVNPr1emREopAEhTiabj\nbbj6/7eB273NJ3vrVF0y9X6ldwDgeiW/BJwUTmTLGUxRpGoUAKTZ7I672r8lE0utCSeyu+CGGLk3\nl4w8Ud+svafQEui9pp+5ZGQtcB7uLuDsOuVLZAMKANJsot467a0LVSo/rUNeepSJpdYCFtjJu2Mp\nuAHXQugb4UR2cl0yJ1JEAUCahncyPRx4E/i/cCK7DW5wwqeo8py/A/AYbmys95p+es8CzsW1Vjq3\nTvkSeY8CgDSTPXAjbN7qtbf/Lq555SUN0PSz1GPeunQsrDTwJHB0OJH9MCJ1pAAgzaRQ/ZMJJ7IT\ngOOAF+huDdRIegwAXr+As3HDpl9Q60yJFFMAkKaQz+cBvohX/YMbWmEY8KNcMtJRx6z15nFv3dNo\nuDncGEGHhhPZPWqXJZENKQBIU1i0Ygm46p+/rH5w5ha4q/8XgZvqma/eZGKpV4GX6SEAeNVVhbGB\nLvZGMRWpOQUAaQpPvPJs4ce/0t2c8vwGvfoveAyYEE3HP1j6Ri4Z+SdunKBPAvvXOmMioAAgTeKJ\nZa5z7boXPrII+Cqu5U9DXv0XKTwH2KWX98/CTeb9E284C5GaUgCQhhdNx0c+89p/AZ7ofH3C6bjj\n9nu5ZKSzvjnrV28tgQDIJSNP4foG7AR8qVaZEilQAJBmsHdHZwddq8bOBw4C7sVVnzS6PgOA51zc\nqKYXhBPZEdXPkkg3BQBpBp8H6Fiy/e64GcC+1YDt/nvyPLAS+FhvCXLJyCLgV7jhLU6sUb5EAAUA\naQ6fH0I7XSvGT8CN9/9kvTPkRyaW6gIeBKZG0/FN+kh6EbAC+H44kR1Xk8yJoAAgDS6ajm8J7Ny5\ncmPID1lO8w2h8G9vvXtvCXLJyBu4ILAJrnezSE0oAEij+yxAx5ubAJztnSybSSEA7NlPusuAJcC3\nNVy01IqvAGCMmWmMedYY85wx5n2TWxvnX8aYNcaY/ylnX5G+dK0d8WWALYZNBLimvrkZkDneus8A\nkEtGVuPubkbSfHc50qT6DQDGmDbgcmA/3AxHRxpjppYkWw6cAvxsAPuK9Ojgc24cGWrr/Ex+3TBO\njXySJmj2+T6ZWOoN3NDQu0fT8f7a+t8APIubOlL/J1J1fu4AZgDzrbULrbUduPlNI8UJrLWvW2sf\nBtaXu69Ib0LD1lwaGtoxpGvNmGenThpf7+wMxr9xQ0P3OfqnN1z0Wbj/yx/XIF8ScH4CwFa4qewK\nFnvb/BjMvhJg4UR2WtuIVV8HaBv5ziX1zs8g+X0OAJD10h8STmT9pBcZsEZ+CJzXQqGte73zUNOl\nqyuf33HSJk+1bbR8CMA1X7zgN81cDpfsd/ZVAPtM2uOq/tLmkpGun5y0954A0yaP/1feDYMa+GOi\nj0VlsWFZlMVPAFiC66RSMMHb5sdg9g1poTBKZL3zUNMlcvrsE+cteo22sW90AY+PG/GBpi6H0/56\nYTvwxj8WzFnszWrWZ/ppk8eHgNuefmE5B582+7M9pGnasqjCorLYsCzK4icAzAWmGGMmGmOG4abg\nm91H+uKMlLuvBJzXBPLitrFvrAq15duAu+qdp8HKxFKduN9jAv08ByjyQ2/9g2rkSQR8BABrbSdw\nMu4AfhqYZa2dZ4w5wRhzPIAxZnNjzEvAd4DvG2MWGWPG9LZvtX4ZaQm/Asa2b/nCA97rpg8Anju8\nta+hn3PJyMPA7cAnw4nsPlXLlQRau59E1to7AVOy7aqin5cBW/vdV6Qn4UT2EOAQ4L62sW9uCawB\n7q9vrirmr956f8DvQ+0LgAOAc4B/VCNTEmyN/BBYAiScyG4E/BpYN2SzRd8PhdgJ+EcmllpT56xV\nRCaWWgY8Anwimo6P8bNPLhmZA9wNfCacyH68mvmTYFIAkEbxY2BL4MJhk57Z1tvWKtU/BXcAQ4FP\nl7FPYeL4cyqfHQk6BQCpu3AiOwOI43rBXow3/DOtFwDu9NYH+t0hl4zch5v/YGY4ke11WGmRgVAA\nkLoKJ7LtwJW41mPfHDnjzvXA54CluIYDrWQO8AoQjabjI8vY70JvfWblsyRBpgAg9XYSsCtwQy4Z\n+QewM7AZcFcmlhpQ55ZGlYml1uPG+xmHe9jt199wTaoPDSeyalAhFaMAIHXjtfm/AHgTON3bXKj+\nubsumaq+a7311/3u4M1+9hPcXdLp/SQX8U0BQOrpF7hB0r6bS0Ze87YVAsA99clSdWViqfnAP4FP\nR9PxyWXseituVNGvLF+xuip5k+BRAJC6CCeyM4HDgX8B1wFE0/FRwCeAx7xmk62qMLbRcX53yCUj\nXcBPgaG3/uP5qmRKgkcBQGounMiOxLX57wTi3skN4JPAMFqv9U+pP+EeBp8STce3KGO/3wFL/jpn\nAeFEtq85hkV8UQCQejgTmAz8IpeMPFG0vVWbf24gE0utxo31M5oyxvrJJSNrgZ+vXtsJcGJVMieB\nogAgNRVOZLfBTXz+MnBeydszgdXAA6X7taDrgOeA46Pp+A5l7HfNmJFDAU4NJ7KjqpIzCQwFAKm1\ni4ARwFm5ZOSdwkbvgeiOwP+1yvAPfcnEUh3A94AhwOXRdNzXcL65ZGTlgXtvC/BBymhJJNITBQCp\nmXAiuztwFPAQ8NuStwu9Y2+raabq68+44SE+h+sJ7Ut478ng7pROCyeyQ6uTNQkCBQCpiXAiG8I1\n+wT4n6IHvwUHeeu/1C5X9eV1dPs68AZwSTQd397PfhuNGQ6uJdE2uDk2RAZEAUBqJYabE/dP3vg2\n7/FGx9wX1/xzcR3yVjeZWGop7up/JDArmo4P97lrElgPnBFOZPV/LAOiA0eqzmv2eTGwDjijhySf\nxTX/DMzVf7FMLJUBrgem49r69yuXjCwEfg9Mo4zB5USKKQBILXwHV11xaS4ZeaGH9wvVP0Gq/y91\nCvAM8K1oOu53nKBCsDjLq2ITKYsCgFRVOJHdAjgLeA34Uen70XS8HYgAr+IGPAukTCy1CojiHu5e\nF03HJ/W3Ty4ZeRo3x/aewN5VzaC0JAUAqbYLgTHAOblk5O0e3t8H16TxZm/y9MDKxFJP4+bQHgek\no+n4MB+7/cRba6hoKZsCgFRNOJH9KHAs8BTdo2CWOtxb/7EmmWp81+OayM7AzZLWp1wy8m/c4HIH\nhBPZnaucN2kxCgBSFUXNPkO4Zp/rS9N41T+H4ap//lnbHDYmr2noibhewoloOn5QP7tA911ATw/Y\nRXqlACDVEsE17fxLLhnpbWz/QvXPn4Ne/VMsE0utxD0PWAvcEE3Ht+5nlzuBJ4AjwolsOUNMS8Ap\nAEjFhRPZYcDPcO3UT+sjaaH6J1P1TDWZTCz1OHAqsAnwh2g63muP36IJY9qARG1yKK3AVwAwxsw0\nxjxrjHnOGNPjbaYx5jJjzHxjzGPGmF2Lti8wxjxujHnUGPNgpTIuDe1kYAqQyiUjz/aUIJqOj8Bd\n5b6Cqn96czUuOO4FnN9P2j8CLwLHei2vRPrVbwAwxrQBlwP74TqdHGmMmVqSZn9gO2vt9sAJQKro\n7S5gX2vtrtbaGRXLuTSkcCK7KW6I47d4/2ifGyQFNgZuUvVPz7znAccBzwNnRtPxz/eW1nvGcjFu\noL2za5NDaXZ+7gBmAPOttQuttR3ALFz9brEIcCOAtfY/wEbGmM2990I+v0dawwXARsC5uWRkeR/p\nvuqtb6h+lppXJpZ6GzeMxnrgf6Pp+Pg+kl8HzAdOCCey5QwxLQHl58S8FfBS0evF3ra+0iwpSpMH\n7jbGzDXG+J4CT5qP1+zzeGAeG94FbsCbBWsm8JDX9l36kImlHgbOAbYErs7n8z2myyUjHbj+AO34\naEIqUosr872stdOBA4CTjDF+eyzmtVD4T693Hvpd8vl8/iPbjX8UCJ133J475pKRdb2lPXqXw5YC\nQ46dHvtYq5VDtZZZh//6oh033R7g0Htf/HevZTH7koNvnjpxY4DD5r34Rt3zXYOl17II4FI2PwFg\nCW4cl4IJ3rbSNFv3lMZau9RbvwbcgqtS8iOkhcL4LvXOQ7/LwafNPvyp55cD5KZP3azXdNF0vO2m\nx29+Flh33SPpD7ZaOVRraWtrC817bf4k4O3rH80QTcen9JQuFAqFnl345t4A3738vn95I4XWPf9V\nXGiAPDRtjfAlAAAOvklEQVTKUjY/AWAuMMUYM9EYMww3/vjskjSzga8AGGP2AN6y1i4zxowyxozx\nto/Gzfn61EAyKo3LG+3zEqCD/psh7gtMBTKZWKqvZwRSIhNLLQROXLN+LcBNXke698klIw/gLrY+\nDvgdWE4CqN8AYK3txDXruwt4GphlrZ1njDnBGHO8l+Z24EVjzH+Bq+iesHpz4H5jzKPAHCBnrW3p\nCb8D6mxgIm6S9/n9pC0cG70+I5A+/f7j23wM3ABwp/eR7ixcQL40nMiOrUXGpPmEenugVGd5BnhL\n04IauizCiexOwCO4Kr9puWRkVW9po+n4h4BFuAuJj3rNHP1q6HKopXfWrsofe+tpr+A6iU3v7UF6\nOJG9ABecL8slI6fWMo81pONiENQ8UwYsnMgOAa7BtTqJ93Xy9xyHmwT9ijJP/lJkzPDR4FpbDcM1\nDe2xKgg3/LYFTgknsnvUKHvSRBQAZDC+CewO/CGXjNzRV8JoOj4SOAnXQex3NchbS8vEUjngJuBj\n9FIVlEtG1uACRQi4xhuiQ+Q9CgAyIOFEdgJwEe6E/h0fu3wV2BRIZWKpd6qZtwA5FVgK/DCajn+k\npwS5ZOSfuLu0j9D3MwMJIAUAKZvXtPA6YCxwei4ZWdZX+mg6PgTXOmgdcFn1cxgMmVjqTdzQK8OA\n6/uoCvoubsylc8OJ7G61yp80PgUAGYgE8DncJO69TfRS7Au4weFuzMRSr1QzY0HjsyroLVwz7XYg\nE05kx9Uuh9LIFACkLN4V5I9xV5THeEMR9yqajrcB5+IGBbyk+jkMJD9VQXfjHgpPAq7VJPICCgBS\nBq89+R9wLXm+nEtGXvOx2xHATrhRP2018xdUPVQF9TZ3wHm4obcPxT2Ql4BTABBfvCvGK4HtgItz\nycj/9bePdyI6H9ch6YdVzWDAeVVBN+Kqgi7sKY03ZPSRwGtAMpzI7lW7HEojUgAQvxLAUbge3T/w\nuc/xuIBxVSaWWlClfEm3U4D/At+NpuMH9JQgl4y8jPs7DgGy4UR2+xrmTxqMAoD0K5zIHgT8FHgZ\nOMwbdrhP3pDPPwLeppcrUqksb+6AwlzCN0bT8Qk9pcslI/fg+nCMB24PJ7IfrF0upZEoAEifwons\nnrhpCdcAX/CuIP24FDcxzJmZWKrPZqJSOZlY6lFcv4zxwKw+Boz7De5h/hRgtjegnwSMAoD0KpzI\n7gLchnu4GM0lI3P97BdNxw/CzWI1Bzc4oNTWlbg5gvfCzdDWm7OB3+MGlrs5nMiOqEHepIFoMLjG\nV5ey8Gb3ugc34NgxuWTkBj/7RdPxibjB4cYAH8vEUk9WKEs6Jrr1WxbRdHwj3N9hMnBEJpZK95Qu\nnMgOB27FzdB2F+4ub3Vls1tVOi4GQXcA8j7hRHYf4F7cyf8bZZz8h+OuPDcBTqngyV/KlImlVuA6\n4K0Eboim43v2lC6XjKz10uVw83XcFk5kR9cso1JXCgCygXAi+yXgr8Bo4OhcMnKdn/284R5uBHbz\n1tdULZPiixeAo8BQIBtNx7ftKZ0XBL6Im0Tm08Dd4UR285plVOpGVUCNryZl4VUFXIzrVfo28EWv\n92i/vN6+1+OGG7gPmJmJpd6tcBZ1THQrqyyi6fiJwK+BZ4C9MrHUWz2lCyeyQ3F/xy8Bi4FDcsnI\nQ4PPblXpuBgE3QFIYXiHR3An/3nAjDJO/qOAWbiT/4PAQVU4+csgZGKpK3Ctsj4M/Cmajvf4sNdr\n3ns0cCawFXBfOJE9umYZlZrTHUDjq1pZeK0+zgHOwJuoBTgjl4z4Gq45mo5vDdyMq/a5D4h4wxJU\ng46JbmWXhVdFdzMQwQ3id1gmllrbW/pwInsAroXQRrjnOqf0N+prnei4GAQFgMZX8bLwZvI6GjdM\nw9bAQuDYXDLyN7+fEU3HvwhcDWwM3ACc0NcJpQJ0THQbUFl4V/634Fr83A7E+pqbwesl/L+4yeXf\nAL4N/La/AQBrTMfFICgANL6KlYV34o/gTvzTcD1GfwWcn0tGVvr5DO+q/5fAIcBq3EnhmhpM8ahj\notuAy6IkCDwOHJyJpRb1lt6b++Ek3OQ/o3F9O872MxZUjei4GAQFgMY36LLwmvUdgztZb4cbmvl/\ngR/mkpGX/HxGNB3fBDgN95xgFPAA8I1MLPXsYPJWBh0T3QZVFt4gfZfhhoNYgRvb6YpMLLW+t33C\niewkIIkbSRRcM+HzgXvrfEeg42IQFAAa34DLwuvJ+w3gy8A4vDFigJ/nkpF+T9zRdDwETC/6jDG4\neQC+B9yQiaW6BpKvAdIx0W3QZeH9bb8O/Ax3bLwE/Am4Hze3QMjbviWwDa6qcEJ+ffum+XUjJuXX\njhyXXzeSrtVjluTfHXNF1zubXOb32VGF6bgYBF8BwBgzE9eKoA241lp7cQ9pLgP2B1YBX7PWPuZ3\n3x7oj9qtrLIIJ7Jb49p0H4UbGhjcSftq4Ne5ZOTVnvbzrgq3wv2z7wT8P1zHoK28JIuBX+Dm9K1H\nT1EdE90qVhbRdHxT3DwBXwI+4GOXLm/ZYIyhzpXjOrtWbPpg5/Itf5ZfO+o2PwMG9pOvIbgqJ4B3\n+7g70XExCP0GAGNMG/Ac8BncaJBzgSOstc8WpdkfONlae6AxZnfgl9baPfzs2wv9UbvlvQG9NsX1\nsB0CdAKvAm+sfnAmwM64k3UE98AO3D/pX4DfALfnkpH1Xv3vdoABdihaJgEf4v1lvhzXKewPwB2Z\nWKqzOr+iLzomulW8LLxe3J8CdgS28L5jBe7i4SVgEbA4E0u96909jAO2y68bfkC+s/0roRGrtguF\nIL++nc43tljb+ebmf+ta8cHfQ+iv/U0c5PUjmeZ9/6eAXXB3HIUg04W7K5kPPIQ7jzwEvOjdheq4\nGCA/AWAP4Fxr7f7e6zOBfPGVvDHmSuDv1tq093oesC+wbX/79qLp/tm9f4oPABO8ZTjuwH0bNwHH\n68AbfZ1Eo+n4GNzojAb3DzFty7GbHbp05auduBP/BvJ58nQMz+c7hrflO4aTXzc8T75tIe3rHhoy\n9o2nQ8PWgbuFn4Q70U/k/eXaSfc/+EveMg94FHimzif9Yk13TFRRw5XF4X84cVJ+zehzQsPWREPt\n68cAdL07hs63NqNr5bgX8mtG/yu/dtS9EHpo6KSnXm7fbPG2uLvMwkm/eEjqZcALuAsQcE1Rt/GW\n4t97+a5bThv/6NKnfwj8B3gwE0u9Uc3fs9X0OFRsia1wJ4WCxcAMH2m28rlvw/FO5psDI3Dd6Ifi\nHnyOx12Fb4K7SppQsozp63PzefKHz4qvIB9aTj70Fvm2t4F2QvmxhLomhNp437jsr69cQdfq0cvz\n60a05deNGEXXkFGE8oTa18HQtaHQsDVdoZErO9tGvz0E988xyVu+WPJRr+CmA3zOW6y3fjETS60r\nv5REuv3xyCsWAF+PpuPH5/Psx/qh3w6NfOfTQ0e9MwQ3IN3kfFfoy4TyhEpCV359+8r82lFzu94d\n+3jnm5s91PXW5i/iqpLfwc0m1wl0to1bNrJ980VTQyNWfSQ0dO20UFt++qNLnx5P0Wxz0XT8OdwF\nzMKi5U3v8wpLB7Cqin1WmoafADAQDXV1MgDneotfy4HncQFuMbAEd6C14+4KPghsmn937L6E8puE\nhq4bR/s6QiH3DDWfh/y6EXStGU1+zWi61owiv3oMXavHsLpjOBDaDHc3scj7nsfovg1+YeSMO/G+\nZ0tv+QDun2Y17tZ5sTdZiEhVeXeMtwO3e3e0n8rn+QTrh00nH5qc72wf0bV+6PD8u2OHd737gdFd\nb29Cfu2osRDaDdeh8Bu9fXbXW5uz7q33hihaA5jf/uhTC4/LnhEGdveWGbi73f7ko+n4gZlY6o5B\n/LpNz08AWIK79SqY4G0rTbN1D2mG+di3J3UNIJlY6oc01Ry2EXD1tSuAWjXLrLVmv6iopKYoC6+T\nWc5bqiWUiaXAzVshZfIzFtBcYIoxZqIxZhhwBDC7JM1s3FgwhWcGb1lrl/ncV0RE6qDfAGCt7QRO\nxk0W8TQwy1o7zxhzgjHmeC/N7cCLxpj/4maAOrGvfavym4iISFkatSOYiIhUmYaDFhEJKAUAEZGA\nUgAQEQmoavUDKJsx5ou4ppc7ArtZax8peu8s4FhgPXCqtfauumSyDowx5wLH4YZ+APietfbOOmap\n5gY4nlRLMsYswDX37QI6rLUN37GyUowx1wIHAcustTt72zYG0rhe7guAqLV2Rd0yWSO9lEXZ54pG\nugN4EjfG/D+KNxpjdsRNbL0jbrC5K4wxTdEOuoJ+bq2d7i1BO/m3AZcD++GGxzjSGDO1vrmqqy5g\nX2vtrkE6+Xuuxx0Hxc4E7rHWGuBvwFk1z1V99FQWUOa5omECgHXm8/5OLhFc89H11toFuAGhgnbg\nBy3gFZsBzLfWLrTWduDmH47UOU/1FKKB/m9ryVp7P25Yh2IR3Ix0eOsv1DRTddJLWUCZ54pmOJBK\nxxNaQvcQxUFxsjHmMWPMb4wxG9U7MzXW2zhTQZUH7jbGzDXGHFfvzDSAzbxOp1hrXwE2q3N+6q2s\nc0VNnwEYY+7GDbJWEMId0N+31lazu3hD66tccBO1n2+tzRtjLgR+jpvIQ4JpL2vtUmPMprhAMM+7\nGhQnyB2byj5X1DQAWGs/N4DdehtnqGWUUS7XUN1xVRqRn7GoAsNau9Rbv2aMuQVXRRbkALDMGLO5\ntXaZMWYLuh+ABo61tnjeBV/nikatAiqux5oNHGGMGWaM2RY3Xv6D9clW7XkHdcGhwFP1ykudaDwp\njzFmlDFmjPfzaNwkQEE7HkK8//zwNe/nrwLZWmeojjYoi4GcKxpmKAhjzBeAX+GGTn4LeKxoIpmz\ncLcyHQSvGeiNwEdxrT8WACcU6jyDwmsG+ku6m4H+pM5ZqgvvAugWXDVHO/C7IJWFMeb3uImmxuMm\njTkXuBX4I66WYCGuGehb9cpjrfRSFp+izHNFwwQAERGprUatAhIRkSpTABARCSgFABGRgFIAEBEJ\nKAUAEZGAUgAQEQkoBQARkYBSABARCaj/D0l0f9NIBP/aAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f39f2b1dbd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(X);\n",
    "sns.kdeplot(Y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 47,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"name": "stderr",
	"output_type": "stream",
	"text": [
	"/usr/local/lib/python2.7/dist-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
	" warnings.warn(self.msg_depr % (key, alt_key))\n"
	]
	}
	],
	"source": [
	"import numpy as np\n",
	"from scipy.stats import norm, laplace\n",
	"import seaborn as sns\n",
	"%matplotlib inline"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 64,
	"metadata": {
	"collapsed": false
	},
	"outputs": [],
	"source": [
	"n=500\n",
	"mu=2.0\n",
	"sigma2=2\n",
	"b=np.sqrt(2)\n",
	"X=norm.rvs(size=n, loc=mu, scale=sigma2)\n",
	"Y=laplace.rvs(size=n, loc=mu, scale=b)"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 65,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"name": "stdout",
	"output_type": "stream",
	"text": [
	"Sample means: 2.04 vs 1.97\n",
	"Samples variances: 4.47 vs 3.32\n"
	]
	}
	],
	"source": [
	"print \"Sample means: %.2f vs %.2f\" % (np.mean(X), np.mean(Y))\n",
	"print \"Samples variances: %.2f vs %.2f\" % (np.var(X), np.var(Y))"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 66,
	"metadata": {
	"collapsed": false
	},
	"outputs": [],
	"source": [
	"np.savetxt(\"two_sample_test_gaussian.dat\",X.reshape(n/2,2))\n",
	"np.savetxt(\"two_sample_test_laplace.dat\", Y.reshape(n/2,2))\n"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 70,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"image/png": 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Brgem49r69yuXjCwEfg9Mo4zB5USKKQBILXwHV11xaS4ZeaGH9wvVP0Gq/y91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\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x7f39f2b1dbd0>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"sns.kdeplot(X);\n",
	"sns.kdeplot(Y);"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": []
	}
	],
	"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": "2.7.6"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 0
	}