gistfile1.txt

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total monthly costs 233.333333333\n",
      "contributions min: 23.333333 avg: 46.666667 max: 93.333333 // weight 2.000000\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "# costs - in EUR\n",
    "insurance = 15 # estimated monthly amount\n",
    "bank_account = 100 / 12.0 # estimated annual amount converted to monthly cost\n",
    "rent = 200\n",
    "internet = 10 # estimated monthly cost\n",
    "\n",
    "# global consts\n",
    "total_monthly_costs = insurance + bank_account + rent + internet\n",
    "print \"total monthly costs\", total_monthly_costs\n",
    "\n",
    "backup_budget_max = 6 # months\n",
    "steepness = 2 # for adjusting the steepness of the weight in relation to the backup budget\n",
    "              # higher values increase steepness, see below for interactive example\n",
    "\n",
    "# dynamic variables\n",
    "backup_budget = 0 # how much we have as a safety cushion, max = backup_budget_max * total_monthly_costs\n",
    "members = 10 # assumption\n",
    "\n",
    "##### don't change anything below\n",
    "\n",
    "# the function\n",
    "def getcontribs(members):\n",
    "    # we want to adjust the total monthly costs in relation to the backup budget,\n",
    "    # see the 3rd cell for a graph on how the weight changes with the backup budget\n",
    "    weight = 1+(steepness**(backup_budget_max-backup_budget/float(total_monthly_costs)))/steepness**backup_budget_max\n",
    "\n",
    "    average_monthly_contrib = (total_monthly_costs / members) * weight\n",
    "    # max and min are relative to average\n",
    "    max_monthly_contrib = average_monthly_contrib * 2\n",
    "    min_monthly_contrib = average_monthly_contrib / 2.0\n",
    "    return min_monthly_contrib, average_monthly_contrib, max_monthly_contrib, weight\n",
    "\n",
    "print \"contributions min: %f avg: %f max: %f // weight %f\" % getcontribs(members)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(4, 58.333333333333336, 116.66666666666667, 233.33333333333334, 2.0),\n",
       " (5, 46.66666666666667, 93.33333333333334, 186.66666666666669, 2.0),\n",
       " (6, 38.88888888888889, 77.77777777777779, 155.55555555555557, 2.0),\n",
       " (7, 33.333333333333336, 66.66666666666667, 133.33333333333334, 2.0),\n",
       " (8, 29.166666666666668, 58.333333333333336, 116.66666666666667, 2.0),\n",
       " (9, 25.925925925925927, 51.851851851851855, 103.70370370370371, 2.0),\n",
       " (10, 23.333333333333336, 46.66666666666667, 93.33333333333334, 2.0),\n",
       " (11, 21.212121212121215, 42.42424242424243, 84.84848484848486, 2.0),\n",
       " (12, 19.444444444444446, 38.88888888888889, 77.77777777777779, 2.0),\n",
       " (13, 17.94871794871795, 35.8974358974359, 71.7948717948718, 2.0),\n",
       " (14, 16.666666666666668, 33.333333333333336, 66.66666666666667, 2.0),\n",
       " (15, 15.555555555555555, 31.11111111111111, 62.22222222222222, 2.0),\n",
       " (16, 14.583333333333334, 29.166666666666668, 58.333333333333336, 2.0),\n",
       " (17, 13.725490196078432, 27.450980392156865, 54.90196078431373, 2.0),\n",
       " (18, 12.962962962962964, 25.925925925925927, 51.851851851851855, 2.0),\n",
       " (19, 12.280701754385966, 24.56140350877193, 49.12280701754386, 2.0),\n",
       " (20, 11.666666666666668, 23.333333333333336, 46.66666666666667, 2.0),\n",
       " (21, 11.11111111111111, 22.22222222222222, 44.44444444444444, 2.0),\n",
       " (22, 10.606060606060607, 21.212121212121215, 42.42424242424243, 2.0),\n",
       " (23, 10.144927536231885, 20.28985507246377, 40.57971014492754, 2.0),\n",
       " (24, 9.722222222222223, 19.444444444444446, 38.88888888888889, 2.0),\n",
       " (25, 9.333333333333334, 18.666666666666668, 37.333333333333336, 2.0),\n",
       " (26, 8.974358974358974, 17.94871794871795, 35.8974358974359, 2.0),\n",
       " (27, 8.641975308641976, 17.283950617283953, 34.567901234567906, 2.0),\n",
       " (28, 8.333333333333334, 16.666666666666668, 33.333333333333336, 2.0),\n",
       " (29, 8.045977011494253, 16.091954022988507, 32.18390804597701, 2.0),\n",
       " (30, 7.777777777777778, 15.555555555555555, 31.11111111111111, 2.0),\n",
       " (31, 7.526881720430108, 15.053763440860216, 30.107526881720432, 2.0),\n",
       " (32, 7.291666666666667, 14.583333333333334, 29.166666666666668, 2.0),\n",
       " (33, 7.070707070707071, 14.141414141414142, 28.282828282828284, 2.0),\n",
       " (34, 6.862745098039216, 13.725490196078432, 27.450980392156865, 2.0),\n",
       " (35, 6.666666666666667, 13.333333333333334, 26.666666666666668, 2.0),\n",
       " (36, 6.481481481481482, 12.962962962962964, 25.925925925925927, 2.0),\n",
       " (37, 6.306306306306307, 12.612612612612613, 25.225225225225227, 2.0),\n",
       " (38, 6.140350877192983, 12.280701754385966, 24.56140350877193, 2.0),\n",
       " (39, 5.982905982905983, 11.965811965811966, 23.931623931623932, 2.0)]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       ""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# below follow examples and explanations on why the getcontrib() is doing how it is doing it\n",
    "\n",
    "# we want to draw some graphs\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# this graph below shows the max/avg/min contribs in case the backup budget is 0\n",
    "# x is the number of members we have, while y is the max/avg/min contribution\n",
    "plt.plot([getcontribs(members) for members in xrange(4,40)])\n",
    "# we also list the numbers members/min/avg/max/weight for illustrative purposes\n",
    "[(members,) + getcontribs(members) for members in xrange(4,40)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hnOWeTejXHQq0Bx6NMj5C+IpV+2+uJZwhnwvsm0Dm77PuRO7OwAzgJcJJn5bR\n662Au6L9+xzQrYz5vhv98s0htFLapnF/Er7eLwLmAX8hjHZIfH8Ckwits68IB6cRhBPOjdp/hIPD\nkui/ZXiZci4hnCB/PnpcX7D+hVHORcAhBa+XtBYUy7nB+68QnchN4f5sAUwE5gOzCFPaxLo/dXGW\niEiGVME9ZUREpKFU9EVEMkRFX0QkQ1T0RUQyREVfRCRDVPRFRDJERV9EJENU9EVEMuT/Abqp0CBC\n0HnSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       ""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# what does the weight do? a graphical explanation\n",
    "tmc=int(math.ceil(total_monthly_costs))\n",
    "steepness=2 # the higher the steeper the curve\n",
    "\n",
    "# x is the variable representing the backup_budget\n",
    "# y is the weight we apply to the average_monthly_contrib variable in the graph below\n",
    "plt.plot([1+(steepness**(backup_budget_max-x/float(tmc)))/steepness**backup_budget_max\n",
    "          for x in xrange(backup_budget_max*tmc)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(4, 29.280598958333336, 58.56119791666667, 117.12239583333334, 1.00390625),\n",
       " (5, 23.424479166666668, 46.848958333333336, 93.69791666666667, 1.00390625),\n",
       " (6, 19.520399305555557, 39.040798611111114, 78.08159722222223, 1.00390625),\n",
       " (7, 16.731770833333336, 33.46354166666667, 66.92708333333334, 1.00390625),\n",
       " (8, 14.640299479166668, 29.280598958333336, 58.56119791666667, 1.00390625),\n",
       " (9, 13.013599537037038, 26.027199074074076, 52.05439814814815, 1.00390625),\n",
       " (10, 11.712239583333334, 23.424479166666668, 46.848958333333336, 1.00390625),\n",
       " (11, 10.647490530303031, 21.294981060606062, 42.589962121212125, 1.00390625),\n",
       " (12, 9.760199652777779, 19.520399305555557, 39.040798611111114, 1.00390625),\n",
       " (13, 9.009415064102564, 18.018830128205128, 36.037660256410255, 1.00390625),\n",
       " (14, 8.365885416666668, 16.731770833333336, 33.46354166666667, 1.00390625),\n",
       " (15, 7.808159722222222, 15.616319444444445, 31.23263888888889, 1.00390625),\n",
       " (16, 7.320149739583334, 14.640299479166668, 29.280598958333336, 1.00390625),\n",
       " (17, 6.8895526960784315, 13.779105392156863, 27.558210784313726, 1.00390625),\n",
       " (18, 6.506799768518519, 13.013599537037038, 26.027199074074076, 1.00390625),\n",
       " (19, 6.164336622807018, 12.328673245614036, 24.657346491228072, 1.00390625),\n",
       " (20, 5.856119791666667, 11.712239583333334, 23.424479166666668, 1.00390625),\n",
       " (21, 5.577256944444445, 11.15451388888889, 22.30902777777778, 1.00390625),\n",
       " (22, 5.323745265151516, 10.647490530303031, 21.294981060606062, 1.00390625),\n",
       " (23, 5.0922780797101455, 10.184556159420291, 20.369112318840582, 1.00390625),\n",
       " (24, 4.880099826388889, 9.760199652777779, 19.520399305555557, 1.00390625),\n",
       " (25, 4.684895833333334, 9.369791666666668, 18.739583333333336, 1.00390625),\n",
       " (26, 4.504707532051282, 9.009415064102564, 18.018830128205128, 1.00390625),\n",
       " (27, 4.33786651234568, 8.67573302469136, 17.35146604938272, 1.00390625),\n",
       " (28, 4.182942708333334, 8.365885416666668, 16.731770833333336, 1.00390625),\n",
       " (29, 4.038703304597702, 8.077406609195403, 16.154813218390807, 1.00390625),\n",
       " (30, 3.904079861111111, 7.808159722222222, 15.616319444444445, 1.00390625),\n",
       " (31, 3.778141801075269, 7.556283602150538, 15.112567204301076, 1.00390625),\n",
       " (32, 3.660074869791667, 7.320149739583334, 14.640299479166668, 1.00390625),\n",
       " (33, 3.5491635101010104, 7.098327020202021, 14.196654040404042, 1.00390625),\n",
       " (34, 3.4447763480392157, 6.8895526960784315, 13.779105392156863, 1.00390625),\n",
       " (35, 3.346354166666667, 6.692708333333334, 13.385416666666668, 1.00390625),\n",
       " (36, 3.2533998842592595, 6.506799768518519, 13.013599537037038, 1.00390625),\n",
       " (37, 3.165470157657658, 6.330940315315316, 12.661880630630632, 1.00390625),\n",
       " (38, 3.082168311403509, 6.164336622807018, 12.328673245614036, 1.00390625),\n",
       " (39, 3.0031383547008548, 6.0062767094017095, 12.012553418803419, 1.00390625)]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       ""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# how does the min/avg/max contribs look when we have x months of backup?\n",
    "backup_budget = total_monthly_costs * 8\n",
    "# this graph below shows the max/avg/min contribs\n",
    "# x is the number of members we have, while y is the max/avg/min contribution\n",
    "plt.plot([getcontribs(members) for members in xrange(4,40)])\n",
    "# we also list the number of members/min/avg/max/weight for illustrative purposes\n",
    "[(members,) + getcontribs(members) for members in xrange(4,40)]"
   ]
  },
  {
   "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": "2.7.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}