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@herrfz
Last active December 11, 2015 16:28
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Coursera Data Analysis -- in Python
{
"metadata": {
"name": "simulation"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Simulation Basics -- equivalent in Python"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import scipy.stats as s"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# normal distribution\n",
"# normal(mean, stdev, size)\n",
"heights = np.random.normal(188, 3, 10)\n",
"print heights"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 190.15026626 187.20390227 187.95763008 187.25140845 191.62472211\n",
" 190.08039721 186.44935175 184.17754141 192.08413107 190.014875 ]\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# binomial distribution\n",
"# binomial(n, p, size)\n",
"coinFlips = np.random.binomial(10, 0.5, 10)\n",
"print coinFlips"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[4 2 4 4 5 5 7 6 7 7]\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# normal density\n",
"x = np.linspace(-5, 5, num=10)\n",
"normalDensity = s.norm.pdf(x, 0, 1)\n",
"print np.around(normalDensity, decimals=2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 0. 0. 0.01 0.1 0.34 0.34 0.1 0.01 0. 0. ]\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# binomial density\n",
"x = np.arange(0, 11, 1) # note that it's (0, 11, 1) instead of (0, 10, 1)\n",
"binomialDensity = s.binom.pmf(x, 10, 0.5)\n",
"print np.around(binomialDensity, decimals=2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 0. 0.01 0.04 0.12 0.21 0.25 0.21 0.12 0.04 0.01 0. ]\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## 'sample' draws a random sample with and without replacement --> numpy.random.choice in numpy 1.7\n",
"## not available in my installed version of numpy\n",
"#\n",
"# heights = np.random.normal(188, 3, 10)\n",
"#\n",
"## with replacement\n",
"# np.random.choice(heights, size=10, replace=True, p=None)\n",
"#\n",
"## without replacement\n",
"# r.choice(heights, size=10, replace=False, p=None)\n",
"#\n",
"## sample according to a set of probability\n",
"# probs = [0.4, 0.3, 0.2, 0.1, 0, 0, 0, 0, 0, 0]\n",
"# sum(probs)\n",
"# np.random.choice(heights, size=10, replace=True, p=probs)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# setting a seed\n",
"np.random.seed(12345)\n",
"print np.random.normal(0, 1, 5)\n",
"print '-------------------------------------------------------------'\n",
"\n",
"np.random.seed(12345)\n",
"print np.random.normal(0, 1, 5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[-0.20470766 0.47894334 -0.51943872 -0.5557303 1.96578057]\n",
"-------------------------------------------------------------\n",
"[-0.20470766 0.47894334 -0.51943872 -0.5557303 1.96578057]\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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