From a81ca9488d258273a52ef2680a9d22a2c5ec3392 Mon Sep 17 00:00:00 2001 From: Zack Cooper Date: Tue, 27 Jan 2015 17:28:50 -0500 Subject: [PATCH] finished project --- charting.ipynb | 434 ++++++++++++++++++++++++++++++++++++++++++++++++ reg_charting.py | 145 ++++++++++++++++ 2 files changed, 579 insertions(+) create mode 100644 charting.ipynb create mode 100644 reg_charting.py diff --git a/charting.ipynb b/charting.ipynb new file mode 100644 index 0000000..163c4d7 --- /dev/null +++ b/charting.ipynb @@ -0,0 +1,434 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:1a7cfeb7cac4c14922932d4d2ed5d109bd4f93b7e6a86e9382eaf4107a57bf00" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import matplotlib.pyplot as plt\n", + "import statistics as st\n", + "import seaborn as sb\n", + "import random\n", + "%matplotlib inline\n", + "\n", + "\n", + "def flip_coin():\n", + " options = ['heads', 'tails']\n", + " return random.choice(options)\n", + "\n", + "def flip_multiple_coins(n = 100000):\n", + " output_list =[]\n", + " count_list = []\n", + " count = 0\n", + " total_flips = [flip_coin() for _ in range(n)]\n", + "\n", + " while 2 ** count <= n:\n", + " total_count =(total_flips[:2 ** count].count('heads') ,\n", + " total_flips[:2 ** count].count('tails'))\n", + " output_list.append(total_count)\n", + " count_list.append(2 ** count)\n", + " count += 1\n", + "\n", + " if 2 ** count != n:\n", + " total_count =(total_flips.count('heads') , total_flips.count('tails'))\n", + " output_list.append(total_count)\n", + " count_list.append(n)\n", + "\n", + " return count_list, output_list\n", + "\n", + "def heads_tails_ratio(a_list):\n", + " count, total = a_list\n", + " return [(heads / tails) for heads, tails in total]\n", + "\n", + "\n", + "def heads_tails_ratio_total(a_list):\n", + " count, total = a_list\n", + " head_count = 0\n", + " tail_count = 0\n", + "\n", + " for heads, tails in total:\n", + " head_count += heads\n", + " tail_count += tails\n", + "\n", + " return head_count / tail_count\n", + "\n", + "def trials_dif_ratio(trials=100000, flips = 100):\n", + " return [heads_tails_ratio_total(flip_multiple_coins(flips))\n", + " for _ in range(trials)]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Line plot of the difference between heads and tails at each recorded point" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "count_list, result_count = flip_multiple_coins()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "diff_count = [(heads - tails) for heads, tails in result_count]\n", + "print(diff_count)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[-1, 0, 0, 0, -2, -2, 8, 12, 8, 32, 52, 54, -86, -30, -88, -62, -48, 254]\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot(diff_count)\n", + "plt.title('Heads/Tails difference')\n", + "plt.xticks(range(0,len(count_list)))\n", + "plt.xlabel('exponential intervals: 2** x')\n", + "plt.ylabel('results at each interval')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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TKSr9TZQMyCU3J/mT5CC6BHE98CIwVkQexS2z8dVYLioi1wBfAuq8Q4cBt6nqbWHnDMct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\nG1t46MV15OVmcd6JsXdMdyY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nrjP3PG/70iAwUETeBJ7AddpW4bZXHCwi7wAvATer6goi\nL1cd7OK60Ply10/gOqnHhR3/NXC9iPwH16b+OG5nsK6WyQ528/ijuD05qnDNZg96r2um9758jKpu\nBSrYf4nvG4BXvGa4T+CagcaHXfsZoF5EVnnvwyOqukpEPusNx+3oBlxT3BMi8rb301V/y8eIyNHA\nF4BrVfURXId2xNdk0pst923SjjcX4anebIdpjIkfq0EYY4yJyGoQxhhjIrIahDHGmIgsQRhjjInI\nEoQxxpiILEEYY4yJyBKEMcaYiCxBGGOMiej/Az6RD899HUvaAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Line plot of ratio of heads to tails at each recorded point" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "ratio_count = [(heads / tails) for heads, tails in result_count]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot(ratio_count)\n", + "plt.title('Percentage more heads than tails')\n", + "plt.xticks(range(0,len(count_list)))\n", + "plt.xlabel('exponential intervals: 2** x')\n", + "plt.ylabel('% more heads compared to tails')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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MBvTIYVj/zgzqlUdaqk20a9q+SAmgVFUXicjxfPqEH8ASgAmzb38lG3eWMmZwV7IyWm1w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\nB+gLzAL+ISL/UtXbm9gvBfg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+ "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Scatter plot (Log scale) of the difference between heads and tails at each recorded point" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.scatter(count_list, diff_count)\n", + "plt.title('Heads/Tails difference (Log Scale)')\n", + "plt.xscale('log')\n", + "plt.xlabel('exponential intervals: 2** x')\n", + "plt.ylabel('results at each interval')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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HZmZmw16usbMkdQELgIXAEmBiM4MyM7NqyPOw4cHANNI85+cCH5P00GAPHBEbAd+StHlE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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Scatter plot (Log scale) of ratio heads to tails at each recorded point" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.scatter(count_list, ratio_count)\n", + "plt.title('Heads/Tails difference ratio (Log Scale)')\n", + "plt.xscale('log')\n", + "plt.xlabel('exponential intervals')\n", + "plt.ylabel('Difference percentage between heads over tails')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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MbHAokjjuBn4aEVvl428FDpL0n7pGZjbIdXZ2vnaT4aRJEzz011pGkRsAzyVNMbIasCow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\nHOd1zc3MmlCRPo4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+ "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below are my thoughts on the above two log scale graphs compared to the first two linear graphs.\n", + "\n", + "There doesn't look to be much difference in the way that we would interpret the two graphs for the raw difference (referring to the log vs linear graphs). Both tell a similar story where as more and more flips occur, the difference increases. This can most likely be attributed to the fact that this is a raw view, so it simply has more observations on the right of the graph.\n", + "\n", + "The percentage different graphs follow the same narrative. Both look to do about the same whether the graphs are linear or logarithmic. One thing I did change, is compare the percentage of heads over tails instead of the raw percentage difference. This tells a more intuitive story (in my opinion) when understanding what occurred more than what.\n", + "\n", + "In conclusion, when comparing raw differences vs percentage differences, you do get a bit more insight into what may be occurring. The more flips that occur (as really visualized in the 'scatter plot difference (log)\" graph, the closer the difference is to 0%. So, as expected, the more someone flips a coin, the more likely they are to average 50/50 split between heads and tails. According to the above, it happens officially around 10^3." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def flip_multiple_coins_dif(n = 100000):\n", + " output_list =[]\n", + " count_list = []\n", + " count = 0\n", + " total_flips = [flip_coin() for _ in range(n)]\n", + "\n", + " while 2 ** count <= n:\n", + " total_heads_count = total_flips[:2 ** count].count('heads')\n", + " total_tails_count = total_flips[:2 ** count].count('tails')\n", + " if total_tails_count == 0:\n", + " total_tails_count +=1\n", + "\n", + " output_list.append((total_heads_count -\n", + " total_tails_count) / total_tails_count)\n", + " count_list.append(2 ** count)\n", + " count += 1\n", + "\n", + " if 2 ** count != n:\n", + " total_heads_count = total_flips[:2 ** count].count('heads')\n", + " total_tails_count = total_flips[:2 ** count].count('tails')\n", + "\n", + " output_list.append(total_heads_count / total_tails_count)\n", + " count_list.append(n)\n", + "\n", + " return output_list\n", + "\n", + "def trials_dif_ratio_simple(trials=100000, flips = 100):\n", + " return [flip_multiple_coins_dif(flips) for _ in range(trials)]\n", + "\n", + "def transpose_results(a_list_of_lists):\n", + " new_list = list(zip(*a_list_of_lists))\n", + " return new_list\n", + "\n", + "def mean_passed_list(passed_list):\n", + " passed_list = transpose_results(passed_list)\n", + " return [st.mean(a_list) for a_list in passed_list]\n", + "\n", + "def str_passed_list(passed_list):\n", + " passed_list = transpose_results(passed_list)\n", + " return [st.pstdev(a_list) for a_list in passed_list]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Graphing 100,000 trials of 100 flips on a histogram\n", + "ratio_many_trials_100 = trials_dif_ratio(flips=100)\n", + "mean = st.mean(ratio_many_trials_100)\n", + "std = st.pstdev(ratio_many_trials_100)\n", + "plt.hist(ratio_many_trials_100)\n", + "ymin, ymax = plt.ylim()\n", + "plt.title('100 flips per 100,000 trials')\n", + "plt.vlines(mean, ymin, ymax)\n", + "plt.vlines([(mean - std), (mean + std)], ymin, ymax, linestyles = 'dashed')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Graphing 100,000 trials of 100 flips on a box plot\n", + "plt.boxplot(ratio_many_trials_100)\n", + "plt.title('100 flips per 100,000 trials')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Graphing 100,000 trials of 1,000 flips\n", + "ratio_many_trials_1000 = trials_dif_ratio(flips=1000)\n", + "plt.hist(ratio_many_trials_1000)\n", + "plt.title('1000 flips per 100,000 trials')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Graphing 100,000 trials of 1,000 flips on a box plot\n", + "plt.boxplot(ratio_many_trials_100)\n", + "plt.title('100 flips per 100,000 trials')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notes on difference between box plots and histograms for 100 flips and 1,000 flips - \n", + "\n", + "Unfortunately I am not able to run the large (1,000 flips) job. I will however hypothesize that it follows a similar trend as the 100 flips charts, but even tighter, because of the law of large numbers." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mean_ratio = mean_passed_list(trials_dif_ratio_simple())\n", + "flip_count, output_list = flip_multiple_coins(100)\n", + "\n", + "plt.scatter(flip_count, mean_ratio)\n", + "plt.title('Mean of Heads/Tails difference per level')\n", + "plt.xscale('log')\n", + "plt.xlabel('exponential intervals: 2** x')\n", + "plt.ylabel('mean at each interval')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mean_std = str_passed_list(trials_dif_ratio_simple())\n", + "\n", + "plt.scatter(flip_count, mean_std)\n", + "plt.title('Standard deviation of Heads/Tails difference per level')\n", + "plt.xscale('log')\n", + "plt.xlabel('exponential intervals: 2** x')\n", + "plt.ylabel('standard deviation at each interval')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/reg_charting.py b/reg_charting.py new file mode 100644 index 0000000..577a50a --- /dev/null +++ b/reg_charting.py @@ -0,0 +1,145 @@ +import matplotlib.pyplot as plt +import statistics as st +import seaborn as sb +import random + + +def flip_coin(): + options = ['heads', 'tails'] + return random.choice(options) + +def flip_multiple_coins(n = 100000): + output_list =[] + count_list = [] + count = 0 + total_flips = [flip_coin() for _ in range(n)] + + while 2 ** count <= n: + total_count =(total_flips[:2 ** count].count('heads') , + total_flips[:2 ** count].count('tails')) + output_list.append(total_count) + count_list.append(2 ** count) + count += 1 + + if 2 ** count != n: + total_count =(total_flips.count('heads') , total_flips.count('tails')) + output_list.append(total_count) + count_list.append(n) + + return count_list, output_list + +def heads_tails_ratio(a_list): + count, total = a_list + return [(heads / tails) for heads, tails in total] + + +def heads_tails_ratio_total(a_list): + count, total = a_list + head_count = 0 + tail_count = 0 + + for heads, tails in total: + head_count += heads + tail_count += tails + + return head_count / tail_count + +def trials_dif_ratio(trials=100000, flips = 100): + return [heads_tails_ratio_total(flip_multiple_coins(flips)) + for _ in range(trials)] + + +# Graphing 100,000 trials of 100 flips on a histogram +#ratio_many_trials_100 = trials_dif_ratio(flips=100) +#mean = st.mean(ratio_many_trials_100) +#std = st.pstdev(ratio_many_trials_100) +#plt.hist(ratio_many_trials_100) +#ymin, ymax = plt.ylim() +#plt.title('100 flips per 100,000 trials') +#plt.vlines(mean, ymin, ymax) +#plt.vlines([(mean - std), (mean + std)], ymin, ymax, linestyles = 'dashed') +#plt.show() + +# Graphing 100,000 trials of 100 flips on a box plot +#plt.boxplot(ratio_many_trials_100) +#plt.title('100 flips per 100,000 trials') +#plt.show() + + +# Graphing 100,000 trials of 1,000 flips +#ratio_many_trials_1000 = trials_dif_ratio(flips=1000) +#plt.hist(ratio_many_trials_1000) +#plt.title('1000 flips per 100,000 trials') +#plt.show() + +# Graphing 100,000 trials of 1,000 flips on a box plot +#plt.boxplot(ratio_many_trials_100) +#plt.title('100 flips per 100,000 trials') +#plt.show() + + + + + + + +def flip_multiple_coins_dif(n = 100000): + output_list =[] + count_list = [] + count = 0 + total_flips = [flip_coin() for _ in range(n)] + + while 2 ** count <= n: + total_heads_count = total_flips[:2 ** count].count('heads') + total_tails_count = total_flips[:2 ** count].count('tails') + if total_tails_count == 0: + total_tails_count +=1 + + output_list.append((total_heads_count - + total_tails_count) / total_tails_count) + count_list.append(2 ** count) + count += 1 + + if 2 ** count != n: + total_heads_count = total_flips[:2 ** count].count('heads') + total_tails_count = total_flips[:2 ** count].count('tails') + + output_list.append(total_heads_count / total_tails_count) + count_list.append(n) + + return output_list + +def trials_dif_ratio_simple(trials=100000, flips = 100): + return [flip_multiple_coins_dif(flips) for _ in range(trials)] + +def transpose_results(a_list_of_lists): + new_list = list(zip(*a_list_of_lists)) + return new_list + +def mean_passed_list(passed_list): + passed_list = transpose_results(passed_list) + return [st.mean(a_list) for a_list in passed_list] + +def str_passed_list(passed_list): + passed_list = transpose_results(passed_list) + return [st.pstdev(a_list) for a_list in passed_list] + + +#mean_ratio = mean_passed_list(trials_dif_ratio_simple()) +flip_count, output_list = flip_multiple_coins(100) + +#plt.scatter(flip_count, mean_ratio) +#plt.title('Mean of Heads/Tails difference per level') +#plt.xscale('log') +#plt.xlabel('exponential intervals: 2** x') +#plt.ylabel('mean at each interval') +#plt.show() + +mean_std = str_passed_list(trials_dif_ratio_simple()) + +plt.scatter(flip_count, mean_std) +plt.title('Standard deviation of Heads/Tails difference per level') +plt.xscale('log') +plt.xlabel('exponential intervals: 2** x') +plt.ylabel('standard deviation at each interval') +plt.show()