{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# **Statistics lecture 1 Hands-on session : solutions notebook**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the companion notebook to lecture 1 in the statistical course series, covering the following topics:\n", "1. numpy/scipy/matplotlib basics\n", "2. Quantiles of the normal distribution\n", "3. Generating data\n", "4. The Poisson distribution\n", "5. Histograms and chi2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Basics\n", "\n", "These notebooks will make use of the numpy/scipy/matplotlib stack. It's also possible to implement these examples with other tools such as `root`, for those who are more familiar with it and have it installed. We'll go with numpy/scipy/matplotlib which has the advantage of being more widely available, and easy to run in tools such as `binder`, but feel free to use other implementations if you like\n", "\n", "To start with, we need to import the relevant python packages:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np # handles most of the numerical work\n", "import scipy.stats # implements statistical tools (PDFs, etc)\n", "from matplotlib import pyplot as plt # for plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "numpy handles most of the underlying work. In particular operations will usually be performed on numpy arrays -- arrays of floats similar to python lists.\n", "For instance we can generate some events as follows:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3.34890993 2.09801312 2.22550667 2.93973333 4.21239699 2.03855857\n", " 1.65910146 4.20389982 4.49855565 2.21596333]\n" ] } ], "source": [ "yvals = np.random.normal(3.0, 1.0, 10) # generate 10 events from a Gaussian(mean=3, sigma=1) distribution\n", "print(yvals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `scipy` package has some useful features like fully-featured PDF implementations, and `matplotlib` will be used for inline plots. As an example of how things work, we can draw a few Gaussian curves: " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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gtnDgbVj7cxi5DB7aDbMeBB8/8PGH4EiY8wO4dx3494VXb4DsDZ6R24voaum+IyMjmTZtGr6+vqads2kzCKWUQ0QexIhOsgMvKqUOich97uPPtbevWbpqPM8ze55h5+md/CblN1w37LpLtpsZM5PH5j7G99d/n4c3PswTqU9gt9mtU9RDKKX4+aqD7Msr4/nbp7BkTHSL7ew24ZspCYQG+vKDN/fxh9VHePSaTgbo5e2C978Ng2fCDX83jEJLDJwA934OLyyEd+6Gb30BfT2bu8cS1jwCRQc8O2b0OFj6x1abdaV031ZgarI+pdRqYHWz11o0DEqpb7TWV9M92FKwhRcPvsgNSTdc1jg0snDwQv7f9P/H77f9nsd2PMZPpv/EfCU9zKvbTvHWrjweWjDsksahKV+ZHMeB/DJe3HyCcXF9uX5SXMcEl+XB/90MwVHwtVcvbRwa8Q+Gr74Mf5sPb98Fd34Idp2zs610pXTfVqC/GRqPUlxTzE82/YSE0AR+nPzjNve7ZeQtnCo/xasZr7IkfglToqaYqKVn2X3qPL/64BALRkbyvUXD29zvJ8tGcbignEfeOcDI6L6MGti3fYKVgnfuAUct3PkBBEW0rV/kSLjmSXj3Xvj813DFr9sn19u04U7fLLpSum8r0Kk2NB5DKcWj6Y9SXlfO/8z7HwJ9AtvV/6HJDxEdFM0ft/8Rp6v1dMhdAZdL8csPDhEZ4s+fvzYRm63tkUm+dhvP3jqZYH8ffvXhoTb7ni9w+H04tcW4wEe2M5Hd+Jtgyjdh85OQu6N9fTWXpDHdd+NnuWfPHgDKysoYOHAgNpuNV155pc3pvvfu3XvRn1XGAbSB0HiQLYVb2Ji3kYcmP8Tw/m2/k24k0CeQH075IUdKjvBu1rsmaOh5PjpQyP68Mn60ZAShge1fLAwP9ue7i5LYml1C2tGzbe/YUAtrH4XIMTD5jnbLBWDxbyFoAHz2S2M2ouk0Vqb7LioqIi4ujj/96U/89re/JS4ujvJyz5ZiRSnVY/6mTJmiuhvr16/3tgoeweVyqVs+ukUtemuRqnPUXbbt5c7Z5XKpO9fcqeb83xxVWlvqYS09S22DQ81+bJ268omNyul0Xbbt5c653uFU8/77c3XFn9KUo5VxLrDpCaV+0VeprM/boXELbH3eGCdzbefGaQFPfrcPHz7ssbHMpLy83NsqXJaW3kdgp7rENVXPIDQeYWPeRg6cO8B94+/Dz97x2H4R4ZHkRyirL+O5fZcMdOsSvLr1FLklNfy/pSPb5Vpqjq/dxsNXjuTY6Ure2ZXXeoeqc7DxcUhaAonzOywXgCnfgH6D4bNfgctDIbeaHoM2EJpO41Iunt77NINCBnHtsGs7Pd7IsJF8JekrvHHkDYqqijygoecpq2ngqc8zmZMUwdzhAzo93tKx0Uwc1I//XXuUmvpW/NNpf4T6Klj8m07LxccP5v8MivbD4VWdH0/To9AGQtNpPjv5GUdKjnD/hPvxtXlm08494+7BhYvXj7zukfE8zd83naCspoEfXznSI+OJCD9ZNorT5XW8sjXn0g2rzsHuf8KkW2HAiEu3aw/jbjTWMj7/LTgbPDOmpkegDYSmU7iUi2f2PsPQ0KEsS1jmsXFjg2NZOHghbx97m+qGao+N6wnqHE5e23qShSMjGRsb6rFxkxPCmDE0jJfTT+J0XWLReOc/wFkHM77tMbnY7LDgZ1ByHA6t8ty4mm6PNhCaTrGlYAvZZdncO/5ej++AvmP0HVTUV7Aqa5VHx+0s/95fSHFVPXfOivf42HfOjCe/tIZ1GacvPuiohx0vGHmUIj0zc7nA8CshbCjs/Ltnx9V0a7SB0HSKN4++SVhAGIuHLPb42BMjJzI+YjyvZbzWpfZFvJyeQ+KAIGYPa+PGtHZwxegoYkIDeHlLzsUHD78PlUUw/X6Py8Vmg6l3G/sqig56fnxNt0QbCE2HKaoqIi0vjeuGXdepyKXLcfuY2zlVcYoNeV0judze3FL25ZVx56x4U9J1+9ht3DpjCJuzisk60yxt9La/GnUdhi3yuFwAJn4dfAKMWYqm23HrrbcyYsQIxo4dy1133UVDQ+fXk7SB0HSYdzPfRSnFjcNvbL1xB1k0eBEDgwbyyuFXTJPRHl5OzyHY34evTO5g7qQ2cPO0Qfj52Hg5/eR/XszdAfm7IPlbxt2+GfQJg7E3wv43jRThmm7FrbfeypEjRzhw4AA1NTW88ELnDb02EJoO4XA5eOfYO8yKncWgkEGtd+ggPjYfbhl5CztP7yTrfJZpctrC2Yo6PtpfwI1T4gj2Ny+NWXiwP9eMj+Gd3XmU17rvArc9Z6TqnniLaXIBSL4HGqpg3xvmyumGdLV0381ZtmwZIoKIkJycTF5eG/bUtIJO1qfpEBtyN3Cm5gw/Hf5T02Vdk3gNT+5+kg+zP+T7U75vurxL8a8dp2hwKm6fOcR0Wd+YFc87u/N4Z1ce35zcDzI+gKl3GSVEzSRmEsROMdxMySu6ZInSx7Y/xpGSIx4dc2TYyDYll+wO6b4bGhp45ZVXePLJJzv+hrjRBkLTId489iZRfaKYGzfXdFkRgRGkxKbwUfZHPDTpIa/Ui1BK8fauPGYMDSNxQLDp8sbFhTIuNpR3dufxTf80cNbDBJNnD41MuxdW3Qc5myBhjjUyuwndId33Aw88wNy5c5kzp/OfnTYQmnZTUFlAekE6D0x4AB+bNV+haxKvYWPeRnac3sGMgTMskdmUfXll5BRXc39qomUyl0+M4bf/zqBm1+sERowwCv5YwejlsPpHcODNLmkg2pNG3tN0pXTfS5Ys4fTp00ydOvXCesOvfvUrzp49y/PPP++R8zX11y0iVwJPYlSFe0Ep9cdmx5cDvwFcgAP4nlJqk/tYDlABOAGHUmqqmbpq2s6aE2sA46JtFalxqYT4hvDh8Q+9YiBW7cnHz27jyrHWVWC7dkIM/1y9gcDC7bDg59a5e/z6wMirjbDaZY+3XoRIc4HGdN9PPfUUIsKePXuYNGkSZWVlxMXFYbPZePnll9uc7vtyfPLJJ196/sILL/DJJ5+wbt06bB4KZDBtkVpE7MAzwFJgNHCLiDSvrbgOmKCUmgjcBTRfdp+vlJqojUPX4uOcjxkfMZ64EPMieZoT4BPA4vjFrD251vKd1Q6ni4/2F7BgZGSHUnp3lMi+AXxngFFPQI37qmVyASP9Rm0ZZH1mrdxujpXpvptz3333cfr0aWbOnMnEiRP59a87XwjKzBlEMpCllMoGEJE3gOXA4cYGSqnKJu2DAJ2UvouTXZbNkZIjPDztYctlX5t4Le9kvsO6U+ssnb1sPl7Mucp6rpsUY5lMAJRiiXMj21wj8Snvy5T+Fsoemgp9wuHA2zDyKgsFd13i4+M5ePA/mwhfeumli45VVFS06N5JSkpi//79F57/4Q9/ACA1NZXU1NQLrz/99NMd1q/RNeVJzDQQsUBuk+d5wPTmjUTkeuAPQCTQ9JuogE9FRAHPK6VWtiRERFYAKwCioqJIS0vziPJWUVlZ2a10Xl26GkHoW9CXtDNpHRqjo+eslCLcJ5yXd75MSK7J0TxNWLm/jkAfsJ0+Qtq5ox0aoyPnHFKeyZSqE7zvupfT/97O7aOtdfUk9UsmOuMj0j9bjdOnT7v7e/K7HRoaSkVFResNvYzT6ezSetbW1rbrMzHTQLTkML1ohqCUeg94T0TmYqxHNG4TTVFKFYhIJLBWRI4opTa20H8lsBJg6tSpqqk17g40xkF3B5RS/O+q/2Vq9FSWL1re4XE6c86H9x7m+X3PM2raKKKCojqsQ1upqXfy7c/Xcu3EQSxeOL7D43TonNesAbs/9UOvZc/JOp6bMxdfu4VblxL84R9rmDOgAia0PxGjJ7/bGRkZhIRYd1PQUSoqKrq0ngEBAUyaNKnN7c38tuUBTXdQxQEFl2rsvvgnikiE+3mB+/8zwHsYLiuNFzlScoSc8hyWJiz1mg5LE5aiUHye+7kl8tZmnKaq3slyq91LLiccfAeGL2HxlOGUVNWzKfOctToMmg6hg+DAW9bKvQQd3UCmMejI+2emgdgBJIlIgoj4ATcDHzRtICLDxJ3QRkQmA35AsYgEiUiI+/UgYDGgM4h5mTUn1uAjPlwx+Aqv6TA0dChDQ4ey7uQ6S+R9uK+A6L4BzEgIt0TeBU5thaqzMOZ6UkcYi+Mf7Lvk/ZU52Gww9gY4/rlRh8KLBAQEUFxcrI1EB1FKUVxc/KXw2rZgmotJKeUQkQeBTzDCXF9USh0Skfvcx58DbgDuEJEGoAb4mlJKiUgUhtupUcfXlVIfm6WrpnVcysXHOR8zM2Ym/QL6eVWXhYMX8uLBFzlfe57+Aeat3FbXO9h47Cy3JA/uVEnRDnHkI7D7Q9IV+PnYuGJ0FJ8eKqLB6bLWzTTuRtj8xH92cnuJuLg48vLyOHv2rNd0aAu1tbXtvghbRUBAwIUNeW3F1H0QSqnVwOpmrz3X5PFjwGMt9MsGLNoVpGkLB84doLCqkAcnPehtVVg0ZBF/O/A30nLTuD7petPkbDx2jjqHi8VjzF/r+BJKQcZHRiSRO7XG4tFRvL0rj+0nSkgxIc34JYkaC/0T4MhqrxoIX19fEhISvCa/raSlpbXLx9/V0cn6NG1i/an12MXOvLh53laFUWGjiAmKYd0pc91Mnx4qIjTQl+T4MFPlXETRfig7BaP+E8o7J2kAAb42PjlkcY1uESPM9cQGqOu60Tkac9AGQtMm0nLTmBI1hVB/z5XY7CgiwoLBC0gvSKeqocoUGQ1OF+uOnGHhqEh8rHTpAGR8CGKDEf8JBgj0szM3aQCfHjptvR9+5FVGLii9aa7XoQ2EplVOlZ/ieNlx5g+a721VLrBoyCIaXA18kfeFKePvOFFCWU0Di0dHmzL+Zcn4CAbPgqAvu5IWj4mmqLyWA/kW12oYNN3YNHfk39bK1XgdbSA0rbI+10gYljoo1buKNGHigImEBYTx2Slz7mo/PXyaAF8b84YPMGX8S1J8HM5mwKirLzq0cGQkdpvw6aEW6lWbic1u1KzO/BScna9Spuk+aAOhaZX1uetJ6p9kae6l1rDb7CwYvICNeRupc9Z5dGylFJ8eKmJO0gAC/SxOLZ7xofF/C+kt+gf5kRwfZv06RKM+tWVwcrP1sjVeQxsIzWUprS1lz5k9Xcq91MjCwQupcdSwrXCbR8c9mF9OQVkti0dbHL0ERnjrwAnQb3CLhxePiSLzTCXZZytbPG4aQ+eDT6B2M/UytIHQXJaN+RtxKRcLBi3wtioXMS16GoE+gWzMuygDS6f49HARNoGFoyw2EJVnIG+HkWr7ElzhNlprD1vsZvLrA4kLjHBXvVmt16ANhOaypOWmERkYyajwUd5W5SL87f5MHzidTfmbPBrZs/bwaabGhxEW5OexMdtEY5TQ8CWXbBLXvw9jYvpabyAARi6D8jwo3Ge9bI1X0AZCc0nqnHVsyt9E6qBUbNI1vypz4+aSX5lPdlm2R8YrLKvhSFEFC0dGemS8dpH5KQRHQ/TlkwIuGBnJ7lPnKau2eMF4+JVG+O3RNdbK1XiNrvmr13QJdhTtoMZR06Wil5ozJ9YoiempcNcNR41UDqkjLDYQTgdkfQ5Ji1qtHJc6YgAuBV9kWZx2IigCYqdA1lpr5Wq8hjYQmkuyKX8T/nZ/pkVP87YqlyQ6KJrh/YezMd8z6xDrj54hJjSA4VHBHhmvzeRth7oySFrcatOJg/rTr48v6494IS/RsCsgf7fXk/dprEEbCM0l2Zy/mWnR0wjw6ZrJxxqZEzuHPaf3UFHfuVQQ9Q4Xm7OKmTciErGq/nMjmZ+CzcfIv9QKdpswJ2kAG46dxeWyeMF42CJAGRleNT0ebSA0LZJbkUtOeQ6zY2d7W5VWmRs3F4dysKVgS6fG2XmyhMo6B/NHWLw5DiBzLQyeCQFtS2Uyf8QAzlXWcaig3GTFmhEzydhVnandTL0BbSA0LbI539gQ1R0MxPgB4+nr17fT4a4bjp7F1y7MsjJbKkBZPpw+CEltr7Mx173DO+3oGbO0ahmbDRIXwvF14HJZK1tjOdpAaFpkU/4m4oLjGBzS8oatroSPzYeUmBQ25W/CpTp+0Vp/9AzT4sMI9jc1C/7FNC76tmH9oZGIYH/Gx4Wy3moDAYYhqy6Ggj3Wy9ZYiqkGQkSuFJGjIpIlIo+0cHy5iOwXkb0islNEZre1r8Y86p31bC/azuzY2db74jvInLg5FNcWk1Gc0aH++aU1HDtdyXyro5fAcNeEDoIBI9vVLXVEJHtzSzlfVW+SYpcgcSEgOpqpF2CagRARO/AMsBQYDdwiIqObNVsHTFBKTQTuAl5oR1+NSew6vYsaR023cC81khKbAsDmgo7lCmp01aRavf7gqIPsNOOuvJ3GuDHcdWOm1eGu4RA7Wa9D9ALMnEEkA1lKqWylVD3wBrC8aQOlVKX6zxbYIEC1ta/GPDbnb8bX5tulw1ubExYQxqiwUaQXpHeof9rRs8T2C2RYpMXhrbnboL7SHR3UPibE9aN/H98LezcsZdgVkL8Lqoqtl62xDDOdrbFAbpPnecD05o1E5HrgD0Ak0JjCsk193f1XACsAoqKiSEtL66zellJZWdnldP6k4BOG+g1l++btpoxv1jnHOeJYV7KOjz//mABb20NzHS7FF0ermRHjw4YNGzyuF1z6nBOyX2GQ2NmcJziLLj7eGiNCXXx2qIDP15/HZqE7MKQijCkoDn/0NGeiWq4y2BW/22bT087ZTAPR0rf1oqBtpdR7wHsiMhf4DbCorX3d/VcCKwGmTp2qUlNTO6qvV0hLS6Mr6VxYWUjRO0XcNuE2UsekmiLDrHPuU9iHtZ+uJSApoF27v7efKKHWuYWb540ndexAj+sFlznno7+AQcnMWbSsQ+OeDc5l69v7iR4xhdExfTunZHtwzYGMPzLar5DRl/gsu9p32wp62jmb6WLKAwY1eR4HFFyqsVJqI5AoIhHt7avxHI0umpSYFC9r0n4mRk4k0Cew3W6mTZlnsQnMTLQ4vLWq2Eh8l9jxTLlzkow1k01Wp92w2WHoPDi+Xmd37cGYaSB2AEkikiAifsDNwAdNG4jIMHGHyYjIZMAPKG5LX405bCncQmRgJIn9Er2tSrvxs/sxNWpquzfMbcw8x4RB/QgN9DVJs0twIg1QnTIQ0aEBJEUG80WmF1JfDJ0PlUVw9oj1sjWWYJqBUEo5gAeBT4AM4E2l1CERuU9E7nM3uwE4KCJ7MaKWvqYMWuxrlq4aA5dysa1wGzNiZnSb8NbmzIqZRU55DvmV+W1qX1bdwP680gt34pZy/HNj53TMpE4NMydpgOEma3B6SLE2kuguInV8vbVyNZZh6j4IpdRqpdRwpVSiUup37teeU0o95378mFJqjFJqolJqplJq0+X6aswloySD0rpSZgyc4W1VOsysmFkAbZ5FbMk+h0vBnCSL3UtKGRfWhHmGu6YTzEmKoM7hYmfOeQ8p10b6DYawRMjWBqKnondSay7QeFGdGTPTy5p0nITQBKL6RLV5HWJj5jmC/X2YOKifuYo151wmlOd3yr3UyPShYfjahS+s3g8BxiwiZzM4LN6sp7EEbSA0F9hasJWk/klEBFp8N+1BRIRZMbPYWrgVp6t1l8umzHPMGBqOr93in0JjNtTEztf67uPnw5Qh/b23DtFQZaQr1/Q4tIHQAFDjqGH3md3MHNh9Zw+NzIqZRUV9BQeLD1623cniKk6VVFvvXgLDQIQNhf7xHhluTtIADheWc7aiziPjtZmEOSB2vQ7RQ9EGQgPA7tO7aXA1dGv3UiPTB05HELYWbL1su8Y7bssNhKMecjZ5xL3USOM5pB+3eBYREGpUmdPrED0SbSA0AGwt3IqvzZcpUVO8rUqn6R/Qn5FhI9la2JqBMNJrJEQEWaSZm7wdhltmaOfdS42MiQmlXx9fNh7zgpspcYGR2bXG4kVyjeloA6EBjAXqSZGTCPQJ9LYqHmHGwBnsO7uP6obqFo87XYr048XMHhZhfUhvdhqIDeI9lwzRbhNSEiPYlHUWZfXGtcT5oFxwwjNlXzVdB20gNJyrOcfR80d7hHupkekDp9PgamDPmZZrFhzIL6Oi1kGKN9YfTmww9j4E9vPosCnDIjhdXsfxs1UeHbdVYqeAX4heh+iBaAOhYVvhNoBuvf+hOZMiJ+Fr871wbs3ZnGW4YmYlhlupFtSWQ97ONtWebi8pw4xzsXwdwu5rzIZOmJPoUOM9tIHQsK1wGyF+IYwKG+VtVTxGH98+TIyceMl1iPTj5xgZHUJEsL+1ip1MB+U0Nsh5mMFhfYjrH3jB+FnK0HlQkg2lp6yXrTENbSB6OUopthVuIzk6GXsnd/R2NaZHT+dIyRHO13558bS2wcmOnPOkWF17Goy7bJ8AGNRi9vpOIWKsQ2w5XozTZfE6RKPBy9aziJ6ENhC9nLyKPAqqCpg+0PMXLG8zI2YGCsX2oi9v4tp18jz1DtcFl4ylZKfB4Bng2/Z6Fe1h1rBwymsdHMwvM2X8SxI5CoIitZuph6ENRC9na5HhgumJBmJM+BiCfYMvWofYnHUOH5uQnGCxgag4DWcOm+JeamSWO2X5ZqvXIUQgYa4RyaTTf/cYtIHo5Wwr3EZkYCQJfRO8rYrH8bH5MDV66kXrEJuPFzNxUD+C/c2sl9UCjWGgJixQNzIgxJ+R0SGkZ3mhFOjQeVB5Wqf/7kFoA9GLcSkX2wu3GzuPu2l679aYMXAGuRW5F9J/l9U0cCCvlFleWX9IM3YeD5xgqphZiRHsyPFC+m+9DtHj0AaiF5N5PpPzded7pHupkcbQ3UY309bsYlwKZlttIJQyLpwJczud3rs1ZieFU+dwsfukxTub+w+B/gnGOoumR2CqgRCRK0XkqIhkicgjLRy/VUT2u//SRWRCk2M5InJARPaKyE4z9eytNLpeerKBGBo6lAGBAy6ca3rWOQJ97Zan9w6sKYKyXFPXHxpJTgjHxybWr0OA4WY6uRmcDutlazyOaQZCROwYVeKWAqOBW0RkdLNmJ4B5SqnxwG+Alc2Oz3cXE5pqlp69mW2F24jvG090ULS3VTENESF5YDLbC7ejlGLz8WKSE8Lw87F28tyvdJ/xwMT1h0aC/X2YMKgfm7yxDpEwD+rKjdxMmm6Pmb+SZCBLKZWtlKoH3gCWN22glEpXSjXOg7cCcSbqo2lCg6uBXad39ejZQyPTo6dTXFvM9vzDZJ2p9Ep4a//z+yEkBsKHWSIvJTGcA3mllNc2WCLvAglzjf9PpFkrV2MKZoZxxAK5TZ7nAZe7Gt0NrGnyXAGfiogCnldKNZ9dACAiK4AVAFFRUaSlpXVGZ8uprKz0is7ZtdlUO6oJLg62XL7V56wcRtjls+v/BUzHvzSHtLTcy3fyqAIuZp3fR1H4NI5ssGYBt0+lE5eCv3+wgUmR1kZrTQ1KoGH3KiqHjep2v8fO4q3fs1mY+c1pKSymxQBpEZmPYSCaprdMUUoViEgksFZEjiilLkoX6TYcKwGmTp2qUlNTO624laSlpeENnTP2ZSCnhW8s/Ab9AvpZKtsb5/zCuy+QW32Sfn1mc/vVC7DZLIzaKjoAGyqJnnkT0RNTLRE50+HkiT2fUhYwkNTUMZbIvEDdVbD9b/QN9GVuN/s9dhZv/Z7NwkwXUx4wqMnzOKCgeSMRGQ+8ACxXSl1wmiqlCtz/nwHew3BZaTzEtsJtjAwbablx8BbJ0cmcbTjMjIR+1hoH+E/YpwUL1I34+9iZFh/GluNeWodw1hFalmG9bI1HMdNA7ACSRCRBRPyAm4EPmjYQkcHAu8DtSqljTV4PEpGQxsfAYuDy9SM1baa6oZp9Z/f1qOytrZEYPBFstQyNK7Ve+IkNVAfGQGispWJnJUZw9HSF9WVIh8wEmw/9SvdbK1fjcUwzEEopB/Ag8AmQAbyplDokIveJyH3uZo8C4cCzzcJZo4BNIrIP2A78Wyn1sVm69jb2nNmDw+XoFQvUjdRWDDUeBGRaK9jZACfTOd9/vLVy8WL6b/8QiJ1iLMxrujVtWoMQkanAHCAGqMG4m/9MKVVyuX5KqdXA6mavPdfk8T3APS30ywbM3W7ai9lWtA0fmw+TIid5WxXL2JvjwNYQw7Fyi8Mv83dDfSWl/cZj7fzBKEPaN8CH9Kxilk+0WHrCPEI2Pg41pR4vjKSxjsvOIETkGyKyG/h/QCBwFDiDsZi8VkRedruJNN2IbYXbGB8xnj6+fbytiiW4XIot2cXEBYxj79m91DktdLmc2AAI5/uPs06mG7tNmDE0nPRs72yYE1zGpjlNt6U1F1MQRjTRDUqp3yulXlBKPa2UekgpNQX4M5BkvpoaT1FWV0ZGcUavWn84UlRBSVU9KbEzqXPWse/MPuuEn9gI0eNw+Pa1TmYTUoZFkFtSQ25Jy7W5TSNuGk6bn65T3c25rIFQSj2jlKpp6ZiI+Cml9iql1pmjmsYMdhTtQKFIHth7gsIaffA3jZuLXeyXrDLnceqrIXfbfzaPeYHGdQjLq8z5+FMWOlon7uvmtGmRWkTSRCS+yfNkjCglTTdjW+E2An0CGR9h/aKpt0g/XszQiCCGRQxgbMRYthW1XKfa4+RuBWe9Jek1LkXigGAiQ/xJ90K46/n+4+FshlEHQ9MtaWsU0x+Aj0XkARH5HfAc8E3z1NKYxbaibUyOmoyv3dfbqlhCg9PFtuxiZrnvpKcPnM6hc4eoqK8wX3j2BrD5wOCZ5su6BCLCrMRw0o+fQ1lcyKe0n/smRLuZui1tMhBKqU+A+4AngbuAZUqp3WYqpvE8p6tOc6LsBDOie8/6w/68UqrqnaS4K63NGDgDp3Kys8iCBMEnNkDcNPAPNl/WZZg1LIJzlfUcO11pqdyKkKFG/Qudl6nb0lYX08+Bp4C5wC+BNBG5ykS9NCbQWJu5N60/bMosRgRmJhoziAkDJhBgDzDfzVRdAgV7vepeaiTFXftik9XrEGKH+DmQrcuQdlfa6mKKAJKVUluUUs8DS4DvmaaVxhS2Fm4l1D+UkWEjva2KZWw+fo6xMaH06+MHgJ/dj8lRky+qU+1xcjYBytL0Gpcitl8gCRFBpFttIMAwkGWn4PwJ62VrOk1bXUzfbRrNpJQ6qZS6wjy1NJ5GKcW2wm0kRydjk95RSLC63sGeU+cvrD80Mn3gdLJKszhXY+IF88QG8A2C2CnmyWgHsxLD2ZpdTIPTZa3gxhmUrjLXLWlto9xKEWlxh487X9JdInKrOappPElOeQ6nq0/3qv0P20+U0OBUF5UXbUwxYmq4a/YGGDILfPzMk9EOZg+LoKreyf68UmsFhw8z6mDocNduSWu3ks8CPxeRDBF5S0SeFZEXReQLIB0IAd42XUtNp2m8GM4c6L2IGqvZnHUOP7uNqUPCvvT6yP4j6evX1zw3U1k+FGd2ifWHRmYmhiNirMlYiojxPpzYCC6LZy+aTtPaRrm9SqmbgGkY5UO/AN4H7lZKTVBKPamUsjhVpKYjbC3YSmxwLHEhvado3+asYqYM6U+gn/1Lr9ttdpKjk9lWuM2c0M8T7rvlod5ff2ikXx8/xsaEeqlOdSrUlMDpA9bL1nSK1lxMy0Xk20qpSqVUGvB94AmMPRE3WqCfxgM4XA52FO1gxsAZiFhcC8FLFFfWcbiw/JLlRWcMnEFhVSG5FSZUlsveAH3CIdLiQj2tMGtYOHtOnae63mGt4Mad5HodotvRmovpYb5cw8EPmAqkAvebpJPGwxwuPkxFQ0WvWn/Ykm24UlKarT80Yto6hFLGhTBhHti6VjDA7GERNDgV209cNgmz5+k7EAaM1OsQ3ZDWvsF+Sqmmt1iblFLFSqlTGIn8NN2ARl97b9r/sDnrHCH+PoyLDW3x+JC+Q4gOiva8gTh3DCqLupR7qZGpQ8Lws9usz8sEhpvpZDo4tEe6O9Gagejf9IlS6sEmTwe0NriIXCkiR0UkS0QeaeH4rSKy3/2XLiIT2tpX03a2Fm5lRP8RhAWEtd64h7A5q5gZieH42Fv+iosIMwbOYFvhNpwup+cEN7pRusD+h+YE+tmZMqQ/m7O8VIbUUQO5262XrekwrRmIbSJyb/MXReRbGJXeLomI2DEWtpcCo4FbRGR0s2YngHlKqfHAb4CV7eiraQM1jhr2nNnTq9xLuSXVnCqpJiWx5fWHRmYOnEl5fTmHiw97Tvjx9dA/HsISPDemB0kZFs7hwnKKKy2+k49PMXZWn9Bupu5Eawbi+8A3RWS9iPyv+y8N+Aat76ROBrKUUtlKqXrgDWB50wZKqXSl1Hn3061AXFv7atrGntN7aHA1MCOm9xiILzINF8rspMtPchvXIbYUbvGMYGcD5HwBiQs8M54JNL4nm63O7hoQamwa1AvV3YrLlhxVSp0BZonIAqAxJOPfSqnP2zB2LNB0/SIPuFwR5LuBNe3tKyIrgBUAUVFRpKWltUG1rkNlZaWpOq86vwo7dqqOVpGWaZ6c9mD2Ob+7p5awACH30A7yDl8+aivON441h9cwvGR4p+WGlh5iUn0lB2siOdfs/Mw+57biUoogX3hr4wH6nj9mqqzm5xxvT2DIybfYvPYjHL7eTWBoFl3lc/YUbapJ7TYIbTEKTWnpl9li0LmIzMcwELPb21cptRK3a2rq1KkqNTW1nWp6l7S0NMzU+ZkPn2FS1CSWLFhimoz2YuY5O12Kh9I+5cqxscyf33pZ8907d/NKxiskpyR3vgTr55tBbIy9+v6L6jCb/Tm3h3kFu9h9spR58+aZGvZ80TkPDYAX/8XsWBeMTr1Ut25NV/qcPYGZcXh5wKAmz+OAguaNRGQ88AKwXClV3J6+mstzruYcR0qOkBKb4m1VLGN/XinltQ7mtOJeamRmzEwcLgc7T3sg/Xf2esON0sw4dDXmJA2gqLyW42etTf9N7BTwC4Hj7b3X1HgLMw3EDiBJRBJExA+4mS/vqUBEBgPvArcrpY61p6+mdS6k14jpPek1vsg8h8il9z80Z3LUZPzt/mwp6OQ6RM15yN8FQ+d3bhwLaMxNtfGYxeGudl9j09zxdTr9dzfBNAOhlHIADwKfABnAm0qpQyJyn4jc5272KBAOPCsie0Vk5+X6mqVrTyU9P51+/v0YFTbK26pYxqZMI713WFDbkuT52/2ZHDm58/shTnwBygWJXd9ADArrQ0JEEF9knrVeeOJ8KD0FJdnWy9a0G1O3eiqlViulhiulEpVSv3O/9pxS6jn343uUUv2VUhPdf1Mv11fTdpRSpBekM3PgzF6T3ruyzsHuU+eZndS22UMjM2NmklWaxZnqMx0Xnr0e/IKNCnLdgDlJEWzNLqHO4cE9IG2hMcJLu5m6Bb3jytELOXb+GMW1xb3KvbT1eDEOl2JOBwwEdDLtxvHPjepp3aTW9+xhEdQ0ONl9stRawWFDod8QY7+IpsujDUQPpdGn3psMxBeZZwn0NXYLt4fh/YcTFhBGekF6xwSXnIDzOV16/0NzZiaGY7cJm7IsdjOJGG6mnC+MfSOaLo02ED2U9IJ0EkMTiQ6K9rYqlvFF1jmmDw3D38feeuMm2MTGzJiZbCnYgkt1oGZBtvtuuBusPzQSEuDL5MH9LmwqtJTEBVBXbizqa7o02kD0QGodtew6vatXzR7yS2vIPlt1UfW4tpISk0JJbQkZJRnt75y1DkIHGdXTuhGzhw3gQH4ZJVX11gpOmAti0+sQ3QBtIHogu0/vpt5V36v2P2w4arhK5g1v2/6H5syKmQXA5vzN7evoqDfSRwxbZLhPuhFzh0egFNZHMwX2N/ZEZK2zVq6m3WgD0QNJL0jH1+bLlKgp3lbFMtKOniG2XyDDIjuWwiE8MJwx4WPabyByt0J9JSRd0SG53mR8XD/69/G9YFwtJXGB4WKqtrg2haZdaAPRA9lcsJnJUZMJ9An0tiqWUO9wsTnrHPNGDOhU6oiU2BT2nd1HeX152ztlfQY23/9UTetG2G3C3OED2HDsLC6XxRvXkhYDSruZujjaQPQwCioLyCrNYk7sHG+rYhk7T5ZQVe8ktYPupUZmx87GqZxsLWhHuGvmZzB4BviHdEq2t5g3fADFVfUcLCizVnDMJAgMg8y11srVtAttIHoYm/I3ATAnrvcYiA1Hz+JrF2Z1cIG6kXER4wjxDWFzQRvdTOUFcOZQt3QvNTLXbVTTrHYz2ewwbKExA3N1IHJMYwnaQPQwvsj7gtjgWBL6ds2CNWaQdvQs0+LDCPZvU3LiS+Jj82FGzAw25W9CtSVXUNZnxv/DFnVKrjeJCPZnfFwoaUc7sYu8oyQthupzULjHetmaNqENRA+i3lnPtqJtzI6dbWoa565EQWkNR09XkDqic+6lRmbHzuZM9RmySrNab5z1GYTEQGT3LnaYOnwAe3NLKa22ONw1cSEghptO0yXRBqIHsfP0TmocNcyN634Lph1lwzHDNZI6ItIj47U53NXpgONphpukmxvjeSMicSms3zQXFG6Eu2Z+aq1cTZvRBqIH8UXeF/jZ/JgW3T0SxnmCtKNnGBgaQFIHw1ubEx0UzbB+w/gi/4vLN8zbAXVl3Xr9oZGJg/rRr4+v9esQYLx/+bugyuISqJo2oQ1ED2JT/iamDZzWy8Jbi0ntZHhrc+bGzWX36d1U1FdculHWWhA7JMzzmFxvYbcJc5K8FO467Ap0uGvXRRuIHkJueS455Tm9Krx118nzVNY5mDfcM+6lRlIHpeJQjstHMx39GIbM6vLV49rKvOEDOFdZx6GCduwB8QQxk6BPhGFwNV0OUw2EiFwpIkdFJEtEHmnh+EgR2SIidSLyo2bHckTkQNNCQppL0+gS6U0GYl3Gafzstnan926N8RHj6effjw25G1puUHrKCG8dfqVH5XoTYxYG646ctlawzdYk3NXi2hSaVjHNQIiIHXgGWAqMBm4RkebhHiXAQ8DjlxhmfvNCQpqW2Zi/kSF9hzC472Bvq2IJSinWZpxmZmI4QZ0Mb22O3WZnTuwcvsj/AofLcXGDox8b/49Y6lG53iQi2J/Jg/vzWYbFBgJg+BKoLjbWdTRdCjNnEMlAllIqWylVD7wBLG/aQCl1Rim1A9CJ4TtBVUMV2wu396ropeNnKzlZXM2i0VGmjD9v0DzK6srYf3b/xQeProbwJAhPNEW2t1g0KoqD+eUUltVYK3jYIiNdydHV1srVtIpnb72+TCyQ2+R5HjC9Hf0V8KmIKOB5pdTKlhqJyApgBUBUVBRpaWkd09ZLVFZWdlrnPVV7aHA10L+4f7c4f0+c87+zjZj9PuePk5Z2wgNafRmXy4UNG6+kv0J5///45e2OalJOfEFe3NVkt+McPHHOZhNaaexo/uv7m1gwuPOV8dpzzuNDx+C/5x12+Hafokst0R0+5/ZgpoFoKaykPSESKUqpAhGJBNaKyBGl1MaLBjQMx0qAqVOnqtTU1A4p6y3S0tLorM6ffvEpoRWhfHPxN/GxmfmRegZPnPPTGemMiXFyw1Lz1lze+fQdsquzv6zroVWgHAxe9C0GD5nV5rE8cc5mo5RiZUYap5xBpKYmd3q8dp1z4K2w5r9IHRsHEd2rrkZTusPn3B7MdDHlAYOaPI8DCtraWSlV4P7/DPAehstK0wyHy8HG/I3Mi5vXLYyDJyiurGPXqfMsGmWOe6mR1LhUssuyyS1vMhE+9rFRzyCu530dRYRFo6JIzyqmqq6FtRczGeFe8Ndupi6FmQZiB5AkIgki4gfcDHzQlo4iEiQiIY2PgcXAQdM07cbsObOHsroy5g/qPuUuO8vnR86gFFxh0vpDI/MGGXscNuS5o5lcTjj2iZFDyN4zjfHCUVHUO13WFxHqNxiixsHRNdbK1VwW0wyEUsoBPAh8AmQAbyqlDonIfSJyH4CIRItIHvAD4GcikicifYEoYJOI7AO2A/9WSn1slq7dmc9PfY6fze9CiojewLqMM0T3DWBMTF9T5QwKGURiaCJpeWnGC7nboaakR4W3NmdqfH9CA335LMMLyftGLjMKMOld1V0GU2+DlFKrgdXNXnuuyeMiDNdTc8qBCWbq1hNQSrE+dz0zYmbQx7ePt9WxhNoGJxszz3L9pFhLEhLOHzyffxz8B2V1ZYQeWwM2HyNuv4fia7cxf8QAPj9yBqdLYbdZmGdqxFLY8BhkfgITv26dXM0l0TupuzGZpZnkV+aTOijV26pYxpbsYqrrnaaFtzZn0eBFOJWT9afWQ8aHRuW4gFBLZHuLRaOjKKmqZ/ep89YKHjgRQgbqdYguhDYQ3Zj1p9YDxmJqb+HjA0UE+/swc2i4JfJGh48mJiiGzzLfhZJsGHWtJXK9ybzhA/Cz2/j4YJG1gkWMWUTW59Bg8V4MTYtoA9GNWZ+7nvER4xnQxzO1ELo6DU4XnxwuYuGoSAJ87ZbIFBEWDllI+tl9VNrsMPJqS+R6k5AAX+YOj2DNgcK2FU7yJCOvhoYqyFpnrVxNi2gD0U3Jq8jjUPEhFg7puf7w5mzLLqG0uoFl4wZaKnfR4EU04OKLwRMguHcY46VjB1JQVsu+PItrVSfMNcKID6+yVq6mRbSB6KasPWlkv1w8ZLGXNbGO1QcL6eNnZ95way/SEyWQCIeTtX37WSrXmywaFYWvXVhzoNBawXZfYxZx9GNoqLVWtuYitIHopnyS8wljw8cSF9JSEFjPw+lSfHKwiAUjrXMvNWLL+IiF1dVsqs6lxtE7fOOhfXxJGRbB6oNecDONuQ7qK+C4djN5G20guiG5FbkcKj7E4vjeM3vYfqKE4qp6y91LABx+n4VBQ6hx1pGen269fC+xbOxAcktqrK8RkTDP7WZ631q5movQBqIbcsG91IsMxJqDhQT42kgdYfEaQPFxOH2AqSO+Qqh/KJ+d+sxa+V7kitFR2G3Caq+4ma4ydlU76qyVrfkS2kB0QxrdS7HBsd5WxRJcLsWag0XMHxFJHz+LU1xkGNlhfMdcz/xB80nLTaPO2TsuWv2D/JiVGM5qb0Qzjb4O6sp1KVIvow1ENyO3IpfDxYdZEr/E26pYxq5T5zlbUcdSb7iXDr0HMZOh32CWJiylsqGSjXkXJRXusSwdO5Cc4moyCi9Tn9sMEuYZGxIPrbJWruZLaAPRzfg051MAroi/wsuaWMcHewvw97GxYKRna0+3ytmjULgPxn0VgOnR0wkPCGd1du/Z6btkjOFm+nB/mxMxewYfP3c002rtZvIi2kB0Mz7J+YRxEeN6jXup3uHio/0FLB4TTbCHS4u2yv43QWww9gbAKEW6NGEpG/I2UF5v8cKtlwgP9mduUgTv78nH5bI6mukrhpsp81Nr5WouoA1EN+J46XEySjJ6lXtpw7GznK9u4PpJMdYKVgoOvAlDUyHkP3mfrhp6FQ2uBtad7D0hmNdNiqWgrJZtJ0qsFTw0FYIiYd8b1srVXEAbiG7Eh8c/xC52rhp6lbdVsYxVe/IJD/JjTpLF0Uu526D0FIy76Usvjwkfw+CQwfw7+9/W6uNFFo+OJsjPzqo9+dYKtvsY7r1jn0C1xcZJA2gD0W1wupx8lP0Rs2JmEREY4W11LKGspoG1Gae5ZkIMvnaLv6r73wSfQBj15dxLIsKyocvYXrSdM9VeqJngBQL97Fw5diCrDxRS2+C0VviEr4GrAQ69a61cDWCygRCRK0XkqIhkicgjLRwfKSJbRKRORH7Unr69jR2nd3C6+jTXJvb8bKKNfHywkHqHi+smWbze4qg3Lkgjl4F/yEWHlyUsQ6FYc6L3VD+7flIsFXUO1lldSCh6PAwYBfv+Za1cDWCigRARO/AMsBQYDdwiIqObNSsBHgIe70DfXsWHxz8kxDekV9V+eG9PPkMjgpgQZ3H9heProOb8Re6lRhJCExgdPrpXuZlmJoYT1def96x2M4nAhJshb7uxaVFjKWbOIJKBLKVUtlKqHngDWN60gVLqjFJqB9DQ3r69ieqGataeXMvi+MUE+AR4Wx1LyC+tYWt2CddZVDnuS+z/FwSGXbZy3DVDryGjJIOjJUctVMx72G3C8omxpB09Q0lVvbXCx30VEMPtp7EUM+MGY4HcJs/zgOme7isiK4AVAFFRUaSlpbVbUW9SWVnZqs7bK7dT46hhUPmgbnd+LdGWc/7ouHERiq7LJS3NurtW3/pyZh7+kIKYJWR9sfmS7fo7++ODD0+lPcWNYTe2Om5bzrmrE+dw4nAp/vT2BhYN8W21vSfPeUK/cQRse4ltzDBmFV2UnvA5N8VMA9HSp9jWQOo291VKrQRWAkydOlWlpqa2UUTXIC0tjdZ0fvXTV4kNjuWuJXdZfzdtAq2ds8uleHR7GtMTQrhp2UzrFANIfxqUg7hrf0Zc1OW9mhs2bGBTwSYen/14qzO7tnzO3YE3T37BzvOK39wxp9XvokfPud8DsOo+UhP8ID7FM2OaQE/5nBsx08WUBwxq8jwOaOt2zM707VHkVeSxvXA7yxOX9wjj0BY2ZZ3jVEk1X58+2FrBSsGulyAuGVoxDgA3DL+BivqKXpXA75bkwRwpqmBPbqm1gkdfC/6hsOsf1srt5ZhpIHYASSKSICJ+wM3ABxb07VG8dewtbGLj+qTrva2KZby+7RRhQX5cOTbaWsGntkBxJkz5RpuaT4uexqCQQbxz7B1z9epCLJ8YS5Cfnde3nbJWsF+QsVh9+H2oOmet7F6MaQZCKeUAHgQ+ATKAN5VSh0TkPhG5D0BEokUkD/gB8DMRyRORvpfqa5auXZV6Zz3vZb5H6qBUooMsvlh6iTPltazNOM2NU+Lw97G2MBC7XgL/vkbBmjZgExtfSfoKO0/vJKcsx0zNugzB/j5cOzGWj/YXUFbTPLbEZKZ+E5z1sPc1a+X2YkzdB6GUWq2UGq6USlRK/c792nNKqefcj4uUUnFKqb5KqX7ux+WX6tvb+PTkp5yvO89NI1oOt+yJvLUrD6dLcUuyxe6l6hIjc+j4m4y71TayPHE5drHzblbv2ch16/TB1Da4rN9ZHTkKhqTAzn+Ay2Wt7F6K3kndhXnz6JsMDhnMjIEzvK2KJbhciv/bfopZieEkRLT9Iu0R9r8Jzro2u5caGdBnAHPj5vJ+1vs0OC2+o/YSY2NDGR8XyuvbTllfJ2LqXXD+BJxIs1ZuL0UbiC7KsfPH2HNmDzeNuAmb9I6PaWPmWfLO11g/e1AKdr5o1H2IHtfu7l8b8TVKakv4OOdjE5TrmtySPJijpyvYfeq8tYJHXQN9wmHH362V20vpHVeebsibR9/E3+7PdcOu87YqlvHPLScJD/JjyRiL11uy1sG5ozD9Wx3qPitmFkNDh/LK4Vesv6P2EtdOiCHE34eX0k9aK9jHHybdZpQjLe+VgY2Wog1EF6SivoIPj3/IlfFXEupvcZoJL5F5uoLPj5zhjpnx+PlY/LXc8hSEDDTqD3QAEeG20beRUZLBztM7Paxc1yTI34ebkwex+kAheeerrRU+5ZuAgu0rrZXbC9EGogvy5tE3qXZU8/VRX/e2Kpbxwhcn8PexcfvMIdYKLjoI2WmQvMKoYtZBrhl6Df38+/HK4Vc8p1sX55spCQjwj8051goOSzBcTTtehNreUbjJW2gD0cWoc9bxasarzBw4k9HhvSM/4ZmKWt7bk89Xp8YRFtTxi3SH2PIM+AYZIZSdIMAngK8O/yppuWmcKrd4j4CXiOkXyNXjB/LG9lPWh7ymfBfqymD3y9bK7WVoA9HF+PD4h5yrOcdd4+7ytiqW8c/0kzS4XNwze6i1gssL4cBbhk87sH+nh7tl5C3YbXZezXjVA8p1D+6dO5Sqeqf1G+dip0D8HNj6VyM9u8YUtIHoQjhdTl469BKjw0czPbqteQ27N9X1Dl7ZepIlo6OJtzq0dcffwOWAGfd5ZLgBfQawLGEZq7JWUVZX5pExuzpjYkKZPSyCf2w+Qb3D4r0Jsx6C8nw42Ht2sluNNhBdiM9zP+dk+UnuHnt3r8m79OaOXMpqGrh3rsWzh9oyI1Ry1NUQ5jnZd465kxpHDS8f6j2uj3vnDuVMRR3v77V441zSFRA5GtL/YoQqazyONhBdBKUULx54kSF9h7Bw8KXrEPQkahucPLchm6lD+jNlSOddPO1iy7NQWwpz/8ujww7vP5zFQxbzWsZrnK+1eI+Al5ibFMGogX15Zn0WDU4LZxEiMOs7cOawUbda43G0gegibC7YzMHig9w55k7sNotzEHmJ17adoqi8lh8sHm6t4OoS2PqsEQkzcILHh79/wv29ahYhInx/URI5xdW8uzvPWuFjb4T+8bD+tzr9hgloA9EFcCkXT+x6grjgOK5LvM7b6lhCVZ2DZ9dnkTIsnFmJEdYKT38K6iog9SemDD+s/zCWxC/h9SOvU1JbYoqMrsYVo6OYMKgff1mXRZ3DaZ1gHz/jcyw6AIffs05uL0EbiC7AmhNrOHr+KN+Z9B187a1X6uoJvJSeQ3FVPT9aPMJawVXnYNvzMPYrbar50FHum3AftY5aXjr0kmkyuhIiwo8WDye/tIb/szqiadyNMGAUfP47cDqsld3D0QbCyziUg6f3PM3IsJFcmXClt9WxhKoGxfMbjrNoVCSTBlu89rDpz+CogXmPmComsV8iSxOW8saRNzhX0zvqF8weFsH0hDCeXn+c6noLL9Q2Oyz8OZQc16nAPYw2EF4mvTKdvMo8vjv5u70mKd+aEw2U1zr4wRUWzx7On4QdL8C4m2CA+eseD0x8gAZnA3/Z/RfTZXUFRIQfLRnBuco6XkrPsVb4iGUQOxU2PAYNtdbK7sGYekUSkStF5KiIZInIRbdsYvAX9/H9IjK5ybEcETkgIntFpEcmuKluqObj0o+ZGjWVlJiuW2fXk5wqrubjnAaunRDD6Ji+1gr/9KcgNljwM0vEDek7hNtG38aqrFWcqusdu6unxYexcGQkz3yexflaiyOaFj5q7IvY9lfr5PZwTDMQImIHngGWAqOBW0SkudN3KZDk/lsBNP9k5yulJiqlppqlpzd5du+zVLgq+P6U7/eafQ+/+vAQPgI/WTbKWsHHP4eMD2HOD6HfoNbbe4hvjf8WYQFhvH3+bVyqd0TZ/Pzq0TQ4Ff86avEO56HzYMRVsOG/oTTXWtk9FDNnEMlAllIqWylVD7wBLG/WZjnwT2WwFegnIgNN1KnLcLTkKK9mvMqs4FmMHzDe2+pYwmeHT7PuyBmWD/MjOjTAOsGOeljzY+ifYMTNW0iwXzDfnfxdTtSd4N/Z/7ZUtreIjwjivnlD2VroZMvxYmuFL/2jsWnuY3PXmHoLZhqIWKCpGc9zv9bWNgr4VER2icgK07T0Ak6Xk19v+TWh/qFc2+9ab6tjCbUNTn754SGSIoO5YoiPtcK3Pw/njsHSx4x6AhazfNhyBvsN5s+7/kxVQ5Xl8r3B/anDiAgUHn3/oLWb5/oNhnkPw5GP4GjvKeBkFmb+UlvymTTfD3+5NilKqQIRiQTWisgRpdTGi4QYxmMFQFRUFGlpaZ1Q2Ro2VWxif8l+7gi/A1WjuoXOneXdzHryzjfw42kB1FbXWHbO/rVnmLbjt5SGT+NggT8UWCO3OVcFXMVz5c/xww9+yM3hN3tFB6v5SryLlRmV/Oyf61iaYF34trjGMbVPHLb3vsOOaU/jslt3U1BZWdmjfs9mGog8oKmzNw5oXgLqkm2UUo3/nxGR9zBcVhcZCKXUSmAlwNSpU1VqaqqH1DeHs9Vn+cmqnzA9ejo/WvwjNmzYQFfXubPszytl9afpXDcxhvtvmERaWpo15+xywcvXgN2XiNteILV/vPkyL0Ua3DnoTl469BK3z7idlNieH5Sg1q8nm2BWZZ7jnmUzSIoKsU54wnPw8tXMdWyEhb+zTKxl322LMNPFtANIEpEEEfEDbgY+aNbmA+AOdzTTDKBMKVUoIkEiEgIgIkHAYuCgibpagku5+Mmmn9DgauCnM37aKxamq+sdfO+NvQwI8edX1461VvjWZ+DkJsMv7U3j4ObBSQ+SGJrIo5sf7RXZXkWE339lHEH+Pnz3jb3WZntNmANT74ItT8Px9dbJ7WGYZiCUUg7gQeATIAN4Uyl1SETuE5HG/MqrgWwgC/gb8ID79Shgk4jsA7YD/1ZKdXuH4j8O/oOthVt5OPlhEkITvK2OJfx+dQYniqv4369OILSPhbvETx+Gdb+GkVfDxFutk3sZ/O3+/G7O7yipLeGP2//obXUsITIkgMduGM/hwnL+tPaYtcIX/w4iRsB790GVxYvlPQRT90EopVYrpYYrpRKVUr9zv/acUuo592OllPq2+/g4pdRO9+vZSqkJ7r8xjX27M/vP7ufpPU+zeMhibky60dvqWMK6jNO8uvUU984ZyqxhFuZbaqiFd1dAQChc86QRI99FGBM+hhXjV/BR9ke9JqrpitFR3JI8mOc3Hrc2qsmvD9zwAtSUwAcP6pTgHaB3bN31MhX1FTy88WEi+0Tyi1m/6BWupVPF1fzorX2MGtiXH1qZrVUp+PC7cPoALH8GgixOBNgG7hl/D1OipvCL9F9wuPiwt9WxhJ9fPYr48CC+9689FJVZuNN54HhY9Es4utrIwaVpF9pAmEyDq4EfbfgRRVVFPDb3Mfr6Wbx72AuU1zZw18s7cCl49tbJ+PtYmL48/S+w/w2Y/1MYvsQ6ue3A1+bL/877X/oH9Oe7679LcU3Pd3/08fPhr7dNprLWwb3/3ElNvYUZX6ffD8OXwic/gczPrJPbA9AGwkSUUvxu6+9IL0jn0ZmPMjFyordVMh2H08WDr+8h51wVz902hQQry4ge+wTW/gLGXO/xQkCeJjwwnCfnP8n52vP8IO0HNDgbvK2S6YyM7stfbpnEwYIyfvjWXlwui1w+Nhvc8Dej+txb34DTh6yR2wPQBsJEXjjwAu9kvsO94+7lK0lf8bY6pqOU4rf/zmDjsbP89rqxzEwMt054wV54+26IHgfLn+1S6w6XYnT4aH4969fsPrObn27+KU6XhXfVXmLhqCh+umwUqw8U8b9rj1on2D8Evv4v8AuC178GFaetk92N0QbCJN7NfJe/7PkLVw29iu9Msja9gzdQSvHHj4/wUnoO98xO4ObkwdYJL9wP/1wOgf3glv8zFie7CcuGLuN7k7/HmhNr+EX6L3pFvqa7ZydwS/Ignll/nL+sy7ROcGgsfP0NqC6GV66HyrPWye6mWJzzoHfwesbr/GH7H0iJSeHXs37d4xellVL8fnUGf/viBLfPGMJPr7IwEV/RAfjnteAXDN/4CELjrJPtIe4edzf1znqe3fcsfnY/fj7j5z36OyMi/Pa6cdQ1uPjT2mO4lOJ7iywKZIiZZNxEvH4zvHQV3PkBhERbI7sbog2Eh/n7gb/zxO4nWDBoAf8z73/ws/t5WyVTcbkMt9KLm09w58wh/PLaMdZd3PJ3was3gm8f+MaHXWIzXEe5b8J91LvqeeHAC9Q76/nFzF/06OqCdpvwP1+dgM0mPPFZJg6n4oeLh1vz3RmaCre9Da/dBP9YCnd+2C1vLKxAu5g8RIOrgce2P8YTu59gWcIyHk99vMcbh4raBla8sosXN5/gmynx1hqHA2/DP5aBf7DxAw8bao1ckxARHpr0EPdPuJ/3j7/PirUrKK0t9bZapmK3Cf99w3i+NnUQT6/P4rtv7LUuuil+Ntz+nlGC9oVFkNcjS850Gm0gPMC5mnPc88k9vJrxKreNuo3fz/49vraee/cHcLK4iq88m876o2f45TWjefTq0dYYB5cLPv8tvHM3xEyGe9dDeKL5ci1ARHhg4gP8Yc4f2Hd2H7euvpXs0mxvq2UqNpvwxxvG8V9LRvDh/gK++nw6BaU11ggfPB2+uRrsfsZMYvc/rZHbjdAGopNsL9zOTR/eREZJBo/NeYwfJ/8Yu83CuH+LUUrx7u48rnlqE2cr6/jnXcl8IyXBGuNwPsdYb9j4PzDpdrjj/S65Ea6zXD30av6+5O9UNlRy00c38VrGaz168VpE+Pb8Ybxwx1RyzlVzzVObWH2g0Brh0eNgRRoMSYEPvgPvfxtqe36erLaiDUQHKasr49HNj3L3p3cT5BvEa8teY9nQZd5Wy1SKymq55+Wd/ODNfQyLDOaDb88mxYoUGkrBzhfhrylGOOu1Txl/Pj3XhTcpchJvX/M2ydHJ/HH7H1mxdgUFlc2TIfcsFo6KYtW3UxjYL4AHXtvNA6/t4lxlnfmC+4TBbe8Y1Qb3vg7PzICja8yX2w3QBqKdOFwO3st8j2tXXcsHxz/g7rF38+Y1b5LUP8nbqplGTb2TZ9OyuOJPG9h8/Bw/v3o0b903i8HhFoST5mw2fMQffR9ip8AD6TD5jm6xz6GzDOgzgGcWPsOjMx9l/9n9XLvqWp7c/SSV9ZXeVs00hkUG894DKfzXkhF8dvgMi/60gRe+yKa2weS1CZvdqGl9z2cQ2B/+72b41+1wzsIw3C6IjmJqIw6Xg9UnVvP8vuc5VXGK8RHjWXnFSkaEjfC2aqZR2+DkrV15/GVdJmcr6lgwMpJHrx5NvBW7o/N3w4bH4NjHEBJj5FWa8HVjV2wvQkT46vCvkhKTwl/2/IUXDrzAu5nvctfYu7gh6QaC/YK9raLH8bXb+Pb8YVwxOopff3jYiJLbdILvLRrOdZNi8fMx8TsQO8VwOW1+Ejb92ahMN+HrMO+/unWUXEfRBqIVzlSfYVXWKt459g4FVQWMDBvJX+b/hdRBqT02Vj23pJpXt53kXztyKa1uYFp8f/5662SmxoeZK9hRDxkfGEnV8raDfygs/AVMv69bbX4zg5jgGP4454/cPup2/rTrTzy+83H+uu+vXD/sem4eeTND+g7xtooeZ3hUCK/eM53NWef474+P8PA7+/nvT45wS/Jgvj59MANDA80R7ONnGIQp3zCMxI4XYN/rMPxKo8ZE4sJec6OiDUQLlNSWsCF3A+tOrWNT/iacysn0gdN5OPlhFgxa0CMNQ1FZLR8fLGT1wSJ25JRgE+GKUVHcMWsIM4eGm3fOzgY4sQEOvQcZH0FtqRGyeuVjMPHrENDzkxu2hzERY/j7kr9z6NwhXsl4hTeOvMGrGa8yJnwMSxOWsnjIYgYGD/S2mh4lZVgEq76dwsbMc7yyJYen12fxzPosZgwNZ+m4gSwZE0VkSIDnBQcPgCt/D7MeNIzE7n8aWWFDB8Poa2HUtRA3rUcbC1E9KEf61KlT1c6d7Y9nrqivYM+ZPew+vZudp3dy4NwBXMpFTFAMS+KXcMPwG0y7Q/NWicKzFXXsOXWeLdnFbDlezJGiCgBGRIWwbNxAbpoWZ84dmqOOXav/yZSIOsMwnEyH+krw7wsjlsG4G3vkHZpZn/OZ6jOszl7Nmpw1F1KHx/eNZ8bAGUwfOJ2xEWOJ6hPllZsas845t6SaN3fm8u8DhWSfrUIERg/sy8yh4cxMDGfioH6EB5tQh9pRD0c+hH1vQHYaOOshKNLYUxGfAkNSSDtUQOr8hZ6XbSIiskspNbXFY2YaCBG5EngSsAMvKKX+2Oy4uI8vA6qBbyildrelb0t0xEDUOeuY9fos6l31+Nh8GBM+hpkxM1k4eCEj+o8w/YdlpoFwuhRnKmrJO1/DibNVZJ+rIvN0BQcLyjhdbkSH+PvYmBYfxszEcJaMiWZYpAd82koZoYLl+VCSbSz0FWdB0X44kwEuh9EuPAmGzjMMQuIC8DXhLrCLYMWNQE5ZDhvzNrKlcAu7Tu+ixmHsJwgPCGd0+GgSQhNICE1gSN8hxAbHMqDPAFP365h9zkopMs9U8snBIjYfP8fuU6UXyprGhAYwJjaUpMhgEiKCGDogiLj+fYgI9sdu88BvurYcMj811shyNkOFEWHmtPljjxlvhM+GJxl7dMKGQt/YLusmvZyBMM3FJCJ24BngCiAP2CEiHyilmlZIWQokuf+mA38Fprexr0fwt/vzyPRHGBIyhHEDxhHoY5JfsxlKKVwKHC5FbYMTl1I4XQqXCxwuF06XosGlaHC4cLhc1Da4qHO4qHM4qal3Ul1v/F9Z56C8toGKWgfnq+spqTL+zlbUcaaiDmeTlMq+diEhvA+zh4YxemAw42NDGB8bjL9NQDnBVQ+VZ4wLuLPecP8468FRa1Rpc9RAfTU0VBt3/bXlUFduGIOqc0YStKqzUF4I9RVfPuHgaIgcCbO+w8HzfoxdfKeRPE3jMeJD44kPjeeOMXfQ4GwgoySDg+cOcqj4EEdKjrC9aDt1zv+EjdrERkRgBOEB4YQFhhEeEE5fv76E+IUQ4hdCkG8QfXz6EOgTiL+PPwH2APzsfvjZ/PC1++Jn88Nus+Nj88EuduxixyY27Dbjf5dy4VIuBDHlRktEGB4VwvCoEL6zMInaBid7TpVyML+MgwVlHMwvY/2RMzia/AbsNiEqxJ8BIf6EBfkRFuRP/z6+hAT4EhLgQ3CAD3387PTxsxPga8ffx06Arw1/Hxs+Nhu+PjZ8bYLd5o9P4nJsScuxC9jLTmLP20bhrtXE2UuQA+9A87rjAf2gb4yxd6dPBPQJN6oeBvQ1ss36BRtpY/z6gE8g+PiDT4Cxkc/uAzZfsPuCzceIuhK7+3+b8dju+cu5mWsQyUCWUiobQETeAJYDTS/yy4F/KmMas1VE+onIQCC+DX09xoLXf0iAqsMFVHlgvPbMyWaicG4wHtvcf80/lEv9tMQtSVBGG/lPW5uA+LtfRyHKZbQvx/g70g4lL4fN1/iC94mAoAEQOcqYEYTGGndN/eMhfNiX1hLOpaVp42AyvnZfxg8Yz/gB4y+85lIuCqsKOVl2ksKqQgqrCimqKqKktoSS2hKyS7OpqK+gssGDYbTuzcmNRqLxX+MX9cJzuHC88XFHaRyDaAiPNia0LqWM/1FUK8hRihOAqjL+PFaO1I5xAYgagDAAERc2FIJy/1+FuCqh8gRS+Z/fcGfp54RP7vF8nQszDUQskNvkeR7GLKG1NrFt7AuAiKwAVrifVoqIhUnmPUIEcM7bSnSOYuBEezr0gHNuN/qcewdeO2e5t8NG9ZILrGYaiJa0bW4uL9WmLX2NF5VaCaxsn2pdBxHZeSn/X09Fn3PvQJ9z98dMA5EHDGryPA5onivgUm382tBXo9FoNCZiZizhDiBJRBJExA+4GfigWZsPgDvEYAZQppQqbGNfjUaj0ZiIaTMIpZRDRB4EPsFYunlRKXVIRO5zH38OWI0R4pqFEeb6zcv1NUtXL9Nt3WOdQJ9z70CfczenR22U02g0Go3n6FnbVTUajUbjMbSB0Gg0Gk2LaAPRhRCRH4mIEpGeVyatGSLyPyJyRET2i8h7ItLP2zqZgYhcKSJHRSRLRB7xtj5mIyKDRGS9iGSIyCER+a63dbIKEbGLyB4R+cjbungKbSC6CCIyCCO1yClv62IRa4GxSqnxwDHg/3lZH4/TJGXMUmA0cIuIjPauVqbjAH6olBoFzAC+3QvOuZHvAhneVsKTaAPRdfgz8DDty9TRbVFKfaqUcmftYyvGXpeexoV0M0qpeqAxZUyPRSlV2JhwUylVgXHB7PF5VUQkDrgKeMHbungSbSC6ACJyLZCvlNrnbV28xF1ATywCfKlUMr0CEYkHJgHbvKyKFTyBcYPn8rIeHkUXDLIIEfkMiG7h0E+BnwCLrdXIfC53zkqp991tforhlnjNSt0sos0pY3oaIhIMvAN8TylV7m19zERErgbOKKV2iUiql9XxKNpAWIRSalFLr4vIOCAB2OfOYBkH7BaRZKVUkYUqepxLnXMjInIncDWwUPXMDTltSTfT4xARXwzj8JpS6l1v62MBKcC1IrIMCAD6isirSqnbvKxXp9Eb5boYIpIDTFVK9egsmO6CUH8C5imlznpbHzMQER+MBfiFQD5GCpmv9+CsAI1FwF4GSpRS3/OyOpbjnkH8SCl1tZdV8Qh6DULjLZ4GQoC1IrJXRJ7ztkKexr0I35gyJgN4sycbBzcpwO3AAvfnutd9Z63phugZhEaj0WhaRM8gNBqNRtMi2kBoNBqNpkW0gdBoNBpNi2gDodFoNJoW0QZCo9FoNC2iDYRGo9FoWkQbCI1Go9G0iDYQGo1JiMg0d72LABEJctdHGOttvTSatqI3ymk0JiIiv8XIzxMI5Cml/uBllTSaNqMNhEZjIiLih5GDqRaYpZRyelkljabNaBeTRmMuYUAwRt6pAC/rotG0Cz2D0GhMREQ+wKgklwAMVEo96GWVNJo2o+tBaDQmISJ3AA6l1Ovu+tTpIrJAKfW5t3XTaNqCnkFoNBqNpkX0GoRGo9FoWkQbCI1Go9G0iDYQGo1Go2kRbSA0Go1G0yLaQGg0Go2mRbSB0Gg0Gk2LaAOh0Wg0mhb5/4Ut6hSzzTeGAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xvals = np.linspace(-5,5,100) # an array of 100 points between -5 and 5 which will be used for plotting\n", "means = [0.0, 1.0, -2.0] # a few mean values to plot\n", "\n", "# Now draw the plots. Note that plt.plot takes 2 arrays, one array of x values and an array of y values.\n", "# norm.pdf is a scalar function, which normally applies to a single x value and returns the value of\n", "# the normal PDF at x. However it can be applied to lists as well, and will return the list of PDF values:\n", "# norm.pdf([x1, x2]) = [norm.pdf(x1), norm.pdf(x2)]\n", "for mean in means:\n", " yvals = [ scipy.stats.norm.pdf(xval, loc=mean, scale=1) for xval in xvals ] # compute the y-values for each x\n", " plt.plot(xvals, yvals, label='mean=%g' % mean) # draw the plots\n", "\n", "plt.ylim(0,0.45) # adjust the y range\n", "plt.grid(True) # draw grid lines on the plot\n", "plt.xlabel('x')\n", "plt.ylabel('G(x)')\n", "plt.title('Gaussian distributions')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now repeat with different widths :" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sigmas = [1.0, 2.0, 3.0] # a few sigma values to plot\n", "\n", "for sigma in sigmas:\n", " yvals = [ scipy.stats.norm.pdf(xval, scale=sigma) for xval in xvals ]\n", " plt.plot(xvals, yvals, label='sigma=%g' % sigma)\n", "plt.ylim(0,0.45) # adjust the y range\n", "plt.grid(True) # draw grid lines on the plot\n", "plt.xlabel('x')\n", "plt.ylabel('G(x)')\n", "plt.title('Gaussian distributions')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can also generate random datasets and plot the result:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", 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\n", 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"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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generate two random variables\n", "xvals = np.random.normal(3.0, 1.0, 10000)\n", "yvals = np.random.normal(50.0, 10.0, 10000)\n", "\n", "plt.subplot(121)\n", "plt.hist(xvals, bins=100, color='b')\n", "plt.subplot(122)\n", "plt.hist(yvals, bins=100, color='b')\n", "plt.figure()\n", "plt.scatter(xvals,yvals, color='b')\n", "plt.figure()\n", "plt.hist2d(xvals, yvals, (30, 30), cmap='Reds');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now compute some sample means, variances and covariances:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample means: 3.002457341667247 50.21797272710719\n", "sample variances: 0.9958065693824414 98.72443476940856\n", "sample RMSs: 0.9979010819627572 9.936017047560282\n", "sample covariance and correlation coefficient: 0.08275101262328706 0.008345906125377296\n" ] } ], "source": [ "mean_x = np.sum(xvals)/len(xvals)\n", "mean_y = np.sum(yvals)/len(xvals)\n", "print('sample means:', mean_x, mean_y)\n", "\n", "var_x = np.sum((xvals - mean_x)**2)/(len(xvals) - 1)\n", "var_y = np.sum((yvals - mean_y)**2)/(len(xvals) - 1)\n", "print('sample variances:', var_x, var_y)\n", "print('sample RMSs:', np.sqrt(var_x), np.sqrt(var_y))\n", "cov_xy = np.sum((xvals - mean_x)*(yvals - mean_y))/(len(xvals) - 1)\n", "cor_xy = cov_xy/np.sqrt(var_x*var_y)\n", "print('sample covariance and correlation coefficient:', cov_xy, cor_xy)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This can also be done more simply using numpy internal functions:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample means: 3.002457341667247 50.21797272710719\n", "sample variances: 0.9958065693824414 98.72443476940856\n", "sample covariance and correlation coefficient: 0.9958065693824416 0.0083459061253773\n" ] } ], "source": [ "print('sample means:', np.mean(xvals), np.mean(yvals))\n", "print('sample variances:', np.var(xvals, ddof=1), np.var(yvals, ddof=1))\n", "print('sample covariance and correlation coefficient:', np.cov(xvals, xvals, ddof=1)[0,1], np.corrcoef(xvals,yvals)[0,1])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the covariance and correlations coefficient should really be zero, the non-zero value here is due to fluctuations. For a case with real correlation, one can do" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample covariance and correlation coefficient of (x, 5x+y): 5.0617838595354945 0.45469868359850607\n" ] }, { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "zvals = 5*xvals + yvals\n", "\n", "plt.hist2d(xvals,zvals, (30,30), cmap='Greens')\n", "print('sample covariance and correlation coefficient of (x, 5x+y):', np.cov(xvals, zvals, ddof=1)[0,1], np.corrcoef(xvals,zvals)[0,1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Gaussian quantiles" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The *quantiles* of a PDF are the fraction of its integral within a given range of its variable. The quantiles of the normal distribution $N(x) = G(x; x_0=0,\\sigma=1)$ play an important role since they are used to define some important quantities later ($1\\sigma$ and $1\\sigma$ errors, $5\\sigma$ discovery, etc.). \n", "\n", "One defines the cumulative distribution function of normal as $\\Phi(x) = \\int\\limits_{-\\infty}^x N(t) dt$, and a two-sided version can also be defined as $\\Phi(x, y) = \\int\\limits_x^y N(t) dt$\n", "\n", "They are easy to compute using the scipy tools:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Draw a normal distribution as before\n", "xvals = np.linspace(-5,5,100)\n", "yvals = [ scipy.stats.norm.pdf(xval) for xval in xvals ]\n", "fig = plt.figure()\n", "plt.plot(xvals, yvals)\n", "plt.ylim(0,0.5)\n", "plt.title(\"Cumulative normal distribution\")\n", "plt.xlabel('x')\n", "plt.ylabel('N(x)')\n", "\n", "# Now fill in part of the distribution and print the integral\n", "up = 1\n", "shaded_xvals = np.linspace(-5,up,100)\n", "shaded_yvals = [ scipy.stats.norm.pdf(xval) for xval in shaded_xvals ]\n", "plt.fill_between(shaded_xvals, shaded_yvals, alpha=0.5, color='g')\n", "plt.text(-4.5, 0.45, 'Phi(%g)=%g' % (up, scipy.stats.norm.cdf(up)), fontsize=20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This form is normally referred to as a *one-sided* quantile. Two-sided quantiles apply the boundary on both sides:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Draw a normal distribution as before\n", "fig = plt.figure()\n", "plt.plot(xvals, scipy.stats.norm.pdf(xvals)) # Can use the function(xvals) syntax for simplicity, same as [ function(xval) for xval in xvals ]\n", "plt.ylim(0,0.5)\n", "plt.title(\"Two-sided quantile\")\n", "plt.xlabel('x')\n", "plt.ylabel('N(x)')\n", "\n", "up = 1\n", "shaded_xvals = np.linspace(-up,up,100)\n", "plt.fill_between(shaded_xvals, scipy.stats.norm.pdf(shaded_xvals), alpha=0.5, color='g')\n", "plt.text(-4.5, 0.45, 'Phi(-%g, %g)=%g' % (up, up, scipy.stats.norm.cdf(up) - scipy.stats.norm.cdf(-up)), fontsize=20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot some quantiles for different values of the bounds. As we'll see, the tail integrals (a.k.a the *survival function*, corresponding to the unshaded areas above) are also useful, so compute all of the following:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Bound1-sided1-tail2-sided2-tail
00.00.5000005.000000e-010.0000001.000000e+00
11.00.8413451.586553e-010.6826893.173105e-01
22.00.9772502.275013e-020.9545004.550026e-02
33.00.9986501.349898e-030.9973002.699796e-03
44.00.9999683.167124e-050.9999376.334248e-05
55.01.0000002.866516e-070.9999995.733031e-07
\n", "
" ], "text/plain": [ " Bound 1-sided 1-tail 2-sided 2-tail\n", "0 0.0 0.500000 5.000000e-01 0.000000 1.000000e+00\n", "1 1.0 0.841345 1.586553e-01 0.682689 3.173105e-01\n", "2 2.0 0.977250 2.275013e-02 0.954500 4.550026e-02\n", "3 3.0 0.998650 1.349898e-03 0.997300 2.699796e-03\n", "4 4.0 0.999968 3.167124e-05 0.999937 6.334248e-05\n", "5 5.0 1.000000 2.866516e-07 0.999999 5.733031e-07" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bounds = [0, 1, 2, 3, 4, 5]\n", "one_sided = [ scipy.stats.norm.cdf(up) for up in bounds ]\n", "one_sided_tail = [ scipy.stats.norm.sf(up) for up in bounds ]\n", "two_sided = [ scipy.stats.norm.cdf(up) - scipy.stats.norm.cdf(-up) for up in bounds ]\n", "two_sided_tail = [ scipy.stats.norm.sf(up) + scipy.stats.norm.cdf(-up) for up in bounds ]\n", "\n", "# Pretty-print the result\n", "import pandas as pd\n", "import jinja2\n", "data = np.array([ bounds, one_sided, one_sided_tail, two_sided, two_sided_tail ]).T\n", "labels = [ 'Bound', '1-sided', '1-tail', '2-sided', '2-tail' ]\n", "pd.DataFrame(data, columns=labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Poisson distributions and the Central-limit theorem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First let's get acquainted with Poisson distributions. As explained in the lecture, they are critical to describe counting processes, and become progressively more Gaussian with increasing event rates, so we can check a few rate hypotheses:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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RateMeanVariance
00.10.10.1
11.01.01.0
23.03.03.0
310.010.010.0
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" ], "text/plain": [ " Rate Mean Variance\n", "0 0.1 0.1 0.1\n", "1 1.0 1.0 1.0\n", "2 3.0 3.0 3.0\n", "3 10.0 10.0 10.0" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xvals = np.linspace(0, 20, 21)\n", "rates = [ 0.1, 1, 3, 10 ]\n", "\n", "for i, rate in enumerate(rates) :\n", " plt.subplot(221 + i)\n", " plt.vlines(xvals, 0, scipy.stats.poisson.pmf(xvals, rate), colors='b', lw=3, alpha=0.5, label='rate=%g' % rate)\n", " plt.legend()\n", "\n", "means = [ scipy.stats.poisson.stats(mu=rate, moments='m') for rate in rates ]\n", "variances = [ scipy.stats.poisson.stats(mu=rate, moments='v') for rate in rates ]\n", "pd.DataFrame(np.array([ rates, means, variances]).T, columns=[ 'Rate', 'Mean', 'Variance' ])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "nexp = 10000\n", "nterms = [ 1, 2, 3, 5, 10, 100 ]\n", "for nterm in nterms :\n", " plt.figure()\n", " data = [ sum([ np.random.poisson(1) for i in range(0, nterm) ]) for k in range(0, nexp) ]\n", " range_max = nterm + 6*np.sqrt(nterm)\n", " plt.hist(data, bins=np.arange(0, range_max, 1), color='b', label='n=%d' % nterm)\n", " xvals = np.linspace(0, range_max, 100)\n", " plt.plot(xvals, nexp*scipy.stats.norm.pdf(xvals, loc=nterm, scale=np.sqrt(nterm)), color='r', label='G(n, sqrt(n))' )\n", " plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the distribution becomes more Gaussian as we increase the number of terms, with a variance that grows as $\\sqrt n$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Histograms and the $\\chi^2$ test\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider a 20-bin histogram of data over $[0,1]$, which we assume is coming from a linear distribution, $f(x) \\propto (1 - x/2)$. We also assume that we have a histogram of data, and would like to decide whether the data is compatible with the assumed linear distribution. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "chi2: 21.20665610969041\n", "p(chi2): 0.38505994102001573\n", "chi2, p(chi2), significance from scipy: 21.206656109690417 0.3850599410200153 0.29221808883742784\n" ] }, { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "nbins = 20\n", "nevts = 1000\n", "np.random.seed(0)\n", "xvals = np.linspace(0.5, nbins - 0.5, nbins)\n", "expected_yields = np.array([ (1 - i/2/nbins) for i in range(0, nbins) ])\n", "expected_yields *= nevts/np.sum(expected_yields)\n", "dataset = [ np.random.poisson(y) for y in expected_yields ]\n", "plt.figure()\n", "plt.bar(xvals, expected_yields, yerr=np.sqrt(expected_yields), color='b')\n", "plt.scatter(xvals, dataset, color='orange', zorder=10)\n", "chi2 = sum( [ ((d-y)/np.sqrt(y))**2 for d,y in zip(dataset, expected_yields) ])\n", "chi2_scipy = scipy.stats.chisquare(dataset, expected_yields, ddof=-1)\n", "print('chi2:', chi2)\n", "print('p(chi2):', scipy.stats.chi2.sf(chi2, 20))\n", "print('chi2, p(chi2), significance from scipy:', chi2_scipy.statistic, chi2_scipy.pvalue, scipy.stats.norm.isf(chi2_scipy.pvalue))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The compatibility between the generated dataset the true distribution may be larger or smaller depending on the random fluctuations that were generated, but generally the agreement should be quite good.\n", "\n", "One can check that the distribution is doing what it is expected by generating datasets:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ndata = 10000\n", "all_data = [ [ np.random.poisson(y) for y in expected_yields ] for i in range(0, ndata) ]\n", "all_chi2 = [ scipy.stats.chisquare(data, expected_yields, ddof=-1).statistic for data in all_data ]\n", "bins = np.linspace(0,50,100)\n", "plt.hist(all_chi2, bins=bins, color='b');\n", "plt.plot(bins, scipy.stats.chi2.pdf(bins, 20)*ndata/2, color='orange')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The p-value we have computed above is the tail integral in the distribution above, and we see that it agrees quite well with the generated datasets.\n", "\n", "If we now consider a prediction with the opposite slope, this will be generally much worse:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "chi2, p(chi2), significance from scipy: 194.2440359156798 1.5427021796274759e-30 11.426428317330783\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "new_dataset = np.flip(expected_yields)\n", "plt.figure()\n", "plt.bar(xvals, new_dataset, yerr=np.sqrt(new_dataset), color='b')\n", "plt.scatter(xvals, dataset, color='orange', zorder=10)\n", "\n", "chi2_scipy_flip = scipy.stats.chisquare(dataset, new_dataset, ddof=-1)\n", "print('chi2, p(chi2), significance from scipy:', chi2_scipy_flip.statistic, chi2_scipy_flip.pvalue, scipy.stats.norm.isf(chi2_scipy_flip.pvalue))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, one can repeat the whole study with a lower number of events per dataset, e.g. 10 instead of 1000. In this regime, the Poisson distributions in each bin are not Gaussian enough, and the computed $\\chi^2$ does not in fact follow a $\\chi^2$ distribution. In this case, one needs to move away from the $\\chi^2$ formula and use a statistical model than accounts for Poisson effects." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Addendum: Correlations and correlation coefficients" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "a = np.random.uniform(-0.5,0.5,10000)\n", "b = np.random.uniform(-0.5,0.5,10000)\n", "u = (a+b)\n", "v = (a-b)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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