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0740CA-2014-1123262014-01-042014-01-08Standard ClassPhillina OberHome OfficeUnited StatesNapervilleIllinois...0.24.271710.26782338127.933JanQ139360.06045NaNNaN
1741CA-2014-1123262014-01-042014-01-08Standard ClassPhillina OberHome OfficeUnited StatesNapervilleIllinois...0.2-64.774810.60893621452.645FebNaNNaNNaNNaN
2742CA-2014-1123262014-01-042014-01-08Standard ClassPhillina OberHome OfficeUnited StatesNapervilleIllinois...0.8-5.487010.13725197859.6638MarNaNNaNNaNNaN
31760CA-2014-1418172014-01-052014-01-12Standard ClassMick BrownConsumerUnited StatesPhiladelphiaPennsylvania...0.24.884010.32270981724.5361AprQ255751.25475NaNNaN
4593CA-2014-1354052014-01-092014-01-13Standard ClassMelanie SeiteConsumerUnited StatesLaredoTexas...0.21.168010.24263370289.3068MayNaNNaNNaNNaN
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4995907CA-2017-1432592017-12-302018-01-03Standard ClassPatrick O'DonnellConsumerUnited StatesNew York CityNew York...0.212.1176120.627346NaNNaNNaNNaNNaNNaN
4996908CA-2017-1432592017-12-302018-01-03Standard ClassPatrick O'DonnellConsumerUnited StatesNew York CityNew York...0.02.7279120.489677NaNNaNNaNNaNNaNNaN
4997909CA-2017-1432592017-12-302018-01-03Standard ClassPatrick O'DonnellConsumerUnited StatesNew York CityNew York...0.219.7910120.430609NaNNaNNaNNaNNaNNaN
49981297CA-2017-1154272017-12-302018-01-03Standard ClassErica BernCorporateUnited StatesFairfieldCalifornia...0.24.5188120.285785NaNNaNNaNNaNNaNNaN
49991298CA-2017-1154272017-12-302018-01-03Standard ClassErica BernCorporateUnited StatesFairfieldCalifornia...0.26.4750120.329097NaNNaNNaNNaNNaNNaN
\n", + "

5000 rows Ɨ 28 columns

\n", + "
" + ], + "text/plain": [ + " Sno Order ID Date of placing order Order Dispatch date \\\n", + "0 740 CA-2014-112326 2014-01-04 2014-01-08 \n", + "1 741 CA-2014-112326 2014-01-04 2014-01-08 \n", + "2 742 CA-2014-112326 2014-01-04 2014-01-08 \n", + "3 1760 CA-2014-141817 2014-01-05 2014-01-12 \n", + "4 593 CA-2014-135405 2014-01-09 2014-01-13 \n", + "... ... ... ... ... \n", + "4995 907 CA-2017-143259 2017-12-30 2018-01-03 \n", + "4996 908 CA-2017-143259 2017-12-30 2018-01-03 \n", + "4997 909 CA-2017-143259 2017-12-30 2018-01-03 \n", + "4998 1297 CA-2017-115427 2017-12-30 2018-01-03 \n", + "4999 1298 CA-2017-115427 2017-12-30 2018-01-03 \n", + "\n", + " Logistics Type Name Segment Country \\\n", + "0 Standard Class Phillina Ober Home Office United States \n", + "1 Standard Class Phillina Ober Home Office United States \n", + "2 Standard Class Phillina Ober Home Office United States \n", + "3 Standard Class Mick Brown Consumer United States \n", + "4 Standard Class Melanie Seite Consumer United States \n", + "... ... ... ... ... \n", + "4995 Standard Class Patrick O'Donnell Consumer United States \n", + "4996 Standard Class Patrick O'Donnell Consumer United States \n", + "4997 Standard Class Patrick O'Donnell Consumer United States \n", + "4998 Standard Class Erica Bern Corporate United States \n", + "4999 Standard Class Erica Bern Corporate United States \n", + "\n", + " City State ... Discount Profit Unnamed: 20 \\\n", + "0 Naperville Illinois ... 0.2 4.2717 1 \n", + "1 Naperville Illinois ... 0.2 -64.7748 1 \n", + "2 Naperville Illinois ... 0.8 -5.4870 1 \n", + "3 Philadelphia Pennsylvania ... 0.2 4.8840 1 \n", + "4 Laredo Texas ... 0.2 1.1680 1 \n", + "... ... ... ... ... ... ... \n", + "4995 New York City New York ... 0.2 12.1176 12 \n", + "4996 New York City New York ... 0.0 2.7279 12 \n", + "4997 New York City New York ... 0.2 19.7910 12 \n", + "4998 Fairfield California ... 0.2 4.5188 12 \n", + "4999 Fairfield California ... 0.2 6.4750 12 \n", + "\n", + " log10000 Total Sales Month Quarter Unnamed: 25 Unnamed: 26 \\\n", + "0 0.267823 38127.933 Jan Q1 39360.06045 NaN \n", + "1 0.608936 21452.645 Feb NaN NaN NaN \n", + "2 0.137251 97859.6638 Mar NaN NaN NaN \n", + "3 0.322709 81724.5361 Apr Q2 55751.25475 NaN \n", + "4 0.242633 70289.3068 May NaN NaN NaN \n", + "... ... ... ... ... ... ... \n", + "4995 0.627346 NaN NaN NaN NaN NaN \n", + "4996 0.489677 NaN NaN NaN NaN NaN \n", + "4997 0.430609 NaN NaN NaN NaN NaN \n", + "4998 0.285785 NaN NaN NaN NaN NaN \n", + "4999 0.329097 NaN NaN NaN NaN NaN \n", + "\n", + " Unnamed: 27 \n", + "0 NaN \n", + "1 NaN \n", + "2 NaN \n", + "3 NaN \n", + "4 NaN \n", + "... ... \n", + "4995 NaN \n", + "4996 NaN \n", + "4997 NaN \n", + "4998 NaN \n", + "4999 NaN \n", + "\n", + "[5000 rows x 28 columns]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.read_excel(r'C:\\Users\\Balakumaran S\\Desktop\\Superstore - Excel.xlsx')\n", + "df" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([ 1., 0., 0., 3., 11., 7., 20., 24., 54., 57., 70.,\n", + " 111., 131., 158., 188., 220., 257., 240., 237., 226., 251., 237.,\n", + " 230., 199., 213., 186., 151., 182., 164., 203., 163., 141., 136.,\n", + " 139., 94., 92., 73., 43., 35., 14., 18., 4., 8., 0.,\n", + " 1., 5., 2., 0., 0., 1.]),\n", + " array([-0.08815426, -0.06461694, -0.04107961, -0.01754229, 0.00599503,\n", + " 0.02953235, 0.05306967, 0.07660699, 0.10014431, 0.12368164,\n", + " 0.14721896, 0.17075628, 0.1942936 , 0.21783092, 0.24136824,\n", + " 0.26490556, 0.28844289, 0.31198021, 0.33551753, 0.35905485,\n", + " 0.38259217, 0.40612949, 0.42966681, 0.45320414, 0.47674146,\n", + " 0.50027878, 0.5238161 , 0.54735342, 0.57089074, 0.59442807,\n", + " 0.61796539, 0.64150271, 0.66504003, 0.68857735, 0.71211467,\n", + " 0.73565199, 0.75918932, 0.78272664, 0.80626396, 0.82980128,\n", + " 0.8533386 , 0.87687592, 0.90041324, 0.92395057, 0.94748789,\n", + " 0.97102521, 0.99456253, 1.01809985, 1.04163717, 1.06517449,\n", + " 1.08871182]),\n", + " )" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(df['log10000'],bins=50)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average 0.4443985447251986\n", + "Variance 0.03232000955459355\n" + ] + } + ], + "source": [ + "x = np.array(df['log10000'])\n", + "m1 = np.average(x)\n", + "ss = np.var(x,ddof=1)\n", + "print(\"Average\", m1)\n", + "print(\"Variance\", ss)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Alpha MME : 2.950580908925828\n", + "Beta MME : 3.688911825575294\n" + ] + } + ], + "source": [ + "#From method of moments\n", + "alphaMM = m1*((m1*(1-m1)/ss)-1)\n", + "betaMM = alphaMM*(1-m1)/m1\n", + "print(\"Alpha MME : \", alphaMM)\n", + "print(\"Beta MME : \", betaMM)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Plotting fit on density histogram\n", + "\n", + "fig,ax = plt.subplots(1,1)\n", + "ax.hist(x,density=True,bins=100)\n", + "xx = np.linspace(0,1,50)\n", + "ax.plot(xx, st.beta.pdf(xx,alphaMM,betaMM),label=\"Beta fit MM\")\n", + "ax.legend(loc='best')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "#Use bootstrap method to find alpha and beta\n", + "\n", + "N= 1000 #Running the simulation 1000 times\n", + "n = 5000 #As we have 5000 samples\n", + "alpha_hat = np.zeros(N)\n", + "beta_hat = np.zeros(N)\n", + "for i in np.arange(N):\n", + " xi = st.beta.rvs(alphaMM,betaMM,size=n)\n", + " m1i = np.average(xi); ssi = np.var(xi)\n", + " alpha_hat[i] = m1i*((m1i*(1-m1i)/ssi)-1)\n", + " beta_hat[i] = alpha_hat[i]*(1-m1i)/m1i\n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([0.10135004, 0.10135004, 0.20270007, 0.40540014, 0.30405011,\n", + " 0.50675018, 0.91215032, 0.50675018, 1.01350035, 1.62160056,\n", + " 1.01350035, 1.82430063, 2.22970077, 1.62160056, 3.95265137,\n", + " 3.54725123, 4.0540014 , 3.04050105, 5.16885179, 4.96615172,\n", + " 5.57425193, 4.86480168, 5.16885179, 6.18235214, 5.776952 ,\n", + " 5.776952 , 5.57425193, 3.54725123, 3.14185109, 2.93915102,\n", + " 2.53375088, 2.63510091, 2.0270007 , 2.33105081, 0.81080028,\n", + " 1.41890049, 1.01350035, 0.91215032, 0.50675018, 0.40540014,\n", + " 0.20270007, 0.10135004, 0.40540014, 0.10135004, 0.10135004,\n", + " 0. , 0.10135004, 0. , 0. , 0.10135004]),\n", + " array([3.46739117, 3.47725796, 3.48712476, 3.49699155, 3.50685835,\n", + " 3.51672514, 3.52659193, 3.53645873, 3.54632552, 3.55619232,\n", + " 3.56605911, 3.57592591, 3.5857927 , 3.5956595 , 3.60552629,\n", + " 3.61539309, 3.62525988, 3.63512668, 3.64499347, 3.65486027,\n", + " 3.66472706, 3.67459386, 3.68446065, 3.69432745, 3.70419424,\n", + " 3.71406104, 3.72392783, 3.73379463, 3.74366142, 3.75352822,\n", + " 3.76339501, 3.7732618 , 3.7831286 , 3.79299539, 3.80286219,\n", + " 3.81272898, 3.82259578, 3.83246257, 3.84232937, 3.85219616,\n", + " 3.86206296, 3.87192975, 3.88179655, 3.89166334, 3.90153014,\n", + " 3.91139693, 3.92126373, 3.93113052, 3.94099732, 3.95086411,\n", + " 3.96073091]),\n", + " )" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Plot histogram of the estimates(alpha,beta) from bootstrap\n", + "\n", + "ax1 = plt.subplot(121)\n", + "ax1.hist(alpha_hat,density=True,bins=50)\n", + "ax2 = plt.subplot(122)\n", + "ax2.hist(beta_hat,density=True,bins=50)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The sample standard deviations of the estimates is a bootstrap estimate for the standard error of the estimator" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.06084364592865924\n", + "0.07449059421438306\n" + ] + } + ], + "source": [ + "print(np.sqrt(np.var(alpha_hat)))\n", + "print(np.sqrt(np.var(beta_hat)))" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.11831024834220828, -0.12187918873784653]\n", + "[0.14758773972765935, -0.15128779226763694]\n" + ] + } + ], + "source": [ + "del1_alpha = np.percentile(alpha_hat - alphaMM, 97.5)\n", + "del2_alpha = np.percentile(alpha_hat - alphaMM, 2.5)\n", + "print([del1_alpha,del2_alpha])\n", + "del1_beta = np.percentile(beta_hat - betaMM, 97.5)\n", + "del2_beta = np.percentile(beta_hat - betaMM, 2.5)\n", + "print([del1_beta,del2_beta])" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2.8322706605836196, 3.0724600976636744]\n", + "[3.5413240858476347, 3.8401996178429307]\n" + ] + } + ], + "source": [ + "#The 95% C.I. works out to(for alpha and beta):\n", + "print([alphaMM - del1_alpha, alphaMM - del2_alpha])\n", + "print([betaMM - del1_beta, betaMM - del2_beta])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using MLE:" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.0393044178574136\n", + "3.791020430224173\n" + ] + } + ], + "source": [ + "#Referred wiki for formulae for estimation of alpha and beta\n", + "\n", + "p = np.sign(x) * (np.abs(x))**(1/n)\n", + "pminusx = (np.abs(1-x)**(1/n))\n", + "G_x = np.prod(p)\n", + "G_1minusx = np.prod(pminusx)\n", + "\n", + "alphaML = 1/2 + G_x/(2*(1 - G_x - G_1minusx))\n", + "print(alphaML)\n", + "betaML = 1/2 + G_1minusx/(2*(1 - G_x - G_1minusx))\n", + "print(betaML)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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mb5/OnB1zTKcS4lek0IXPFFQUMGrJ/bRyOjnv4LlMc19uOpJvtRsAV4zlr99v4iJ7ImPWjWFD9gbTqYT4hazlInxCa83fl/2V/KoiRmbHMNp5O8Fygeajz2DdO+YOrEUHeH7VS9zYpj1/WfYX5gyYQ1pUmsGEQlSTQhe1+nWJ1b2U7PvbZ/JF9jr+WuLinyX34/Kjf1r13Zc6XfIYsQU/MW7HXG5smc4DSx9gWv9phFnD6n6sEA1IDrmIU6bsOTy39gUuKKvgswO3kUOQr1KoFAx6hTZNOvPc4Vy25W3jpcyXTKcSQgpdnCoPzU+bgkO7aXmoG2s855oO1DjsDvjDDPqoaIaXe5i5YyaL9i4ynUqEOCl0cUpSEhdREHmEwXkOplbeYDpO44ppAkNn8kBuLufpMJ786kn2FcmSu8IcKXRRp5+Xtj12eVurPQdPyjK6l1Xxbt6f8ITiP6emHbEP+Ddjs37A4qrkweUP4nQ7TacSISoE/wcK39C0Pu0NwrUHdfAKDpJiOpA5nYZyWufbePrQAb7N+5YJmyb8ctfxfhgK0RCk0MVJaR63mOzIIvrkJbCwqq/pOOZd9jx9Es/lutJKpmybwrqD60wnEiFICl3Um9VajKfJF5xT4eKjvHtNx/EPtjAYPIWHiytp5VGMXjGawspC06lEiPGfycIiYJzb5E1+tGgcB/tRQJzpOKfEV4dCfn6efpbbecH9CsOaaZ5b+xxwkU+eXwhvyAhd1EuzyA3sicumV0EUyyouNR3H73zuyaB95zu5+8gRPvnhE2wxW01HEiFECl3Ug5u4Ju+T6nKzOvtuguXUfp/r9xR3OFpyjtNNRNpclLXYdCIRIqTQhdcyEt5hn8NDi5wO5OompuP4L1s49msn84/cAmyWcsKbzgO06VQiBMgxdOGVGEsuh1K+5qxyC8sLbjQd56Q12vTB1LNpc8lT3L/yKV5K+hZX7BZgQOO8tghZUujCK+enTuZriyLy0LV4sJqOUyu/m+vd5U6af/Q250Rl822TeeRXjCTRkWg6lQhicshF1Klt+Ca2xOdzblEC31V0NR0ncCjFaOcIHs4px2KtYMza500nEkFOCl3UQZOW+i5hGrZm3246TMDJIYEpZTdzd0EBn+79jGX7lpmOJIKYFHqIq+vU9J5RH/N1tJsW+WdQ7E5t5HTBYYGnO03z2nFmlZNnv3qSUmep6UgiSEmhi+NyUE556pckumBj7nDTcQLaU87beLLEw+HyfF7ZMM50HBGk6ix0pdQUpdRhpdS249zfWylVqJTaVPPxhO9jChP6xb/Ndw4rYTk98GiH6TgB7QixdLzsRW4oLmbmzllYHLLMrvA9b0boU4G6rva7Qmvdqebj6VOPJUxLIZfdyd+RVmljV4EPLtsmoP1V3J/agxSXm7imcwC36UQiyNRZ6Frr5UB+I2QRfqR34lSy7DaKD1+JHJnznZgrX2Z0cRUuRy5hiatMxxFBxlf/U7srpTYrpT5VSp1zvI2UUiOUUplKqcycnBwfvbTwtYoDm9iQdIim5REcKulmOk5wiU6lT+9n6VVWTlTKQpRNVmQUvuOLQt8ItNJadwReAT443oZa60la6wytdUZKSghfEMHPzVr8F3JsNrKzByPrtfie6vgH+hxOxYKL+CZzTccRQeSUC11rXaS1Lqn5/BPArpRKPuVkwojiXQuZ7DpE09IECsuP+8uWOBVK8XLFXdxWUIordierslaaTiSCxCmf+q+USgOytdZaKdWV6h8SeaecTDQ+rZm+/AkKbVZyD//BdBq/dypLDWTpVPLyLiM9ehnPrfwb867/nDBrmA/TiVDkzbTFWcBq4CylVJZS6g6l1Eil1MiaTQYD25RSm4HxwBCttSwtF4CKtr3H26qES2LPoKIi3XScoPeW6wqG5obxU2U+b22eBMg1SMWpqXOErrUeWsf9rwKv+iyRMMKCh7fXPEdxmIV7ez3L/LV7TUcKem6szC66kz5x45i09U0GnDXYdCQR4GS1RQHAANtSptuqSCpuxmVj95qOE9DqM7reotswsUV/BuUuZeyKvwHXNlwwEfRkgrHAjosmSZ9QYrGwL0dGiY3ttH7/4M5yDwuz12GL3GU6jghgUuiCQfbFfBRvJb64Be7KZqbjhB5HHLf1fJJmThdN0mYjZ5CKkyWFHuLCcJKauIhSi4X9OdeYjhOS0kd9zFkzo7kyN4ai8FISEpaZjiQClBxDD3HX2BfzYZyV2OLmFFeeZjqO32j8WSaKuYV30iX+RbamfAFFcoauqD8ZoYcyZwVpCYsoslo5mHuV6TQh7wfdjPTDnXBa3LRIecd0HBGApNBDWFnmm8yLtxFdchqeiham4whgZtlQrihyURi/g+9yt5uOIwKMFHqoclXy/sbXOGK1cjh3oOk0okYF4Rw8fC0xHg//XPoXfj5HT044Et6QY+ghyrlxGtMcmqiyVIrLW5uOI46y1HUht+Uv5j1rFuf/42mOlGSYjiQChIzQQ5GrigXrx5Nts5GTKxev8D+KZXm307rKSWyTDwCX6UAiQEihhyD35plMCXPRLqoZ7tK2puOIWvygW3BOTlvyw1y0TppvOo4IEFLoocbtYsnaf7E3zM7tv/szst65/5pfdAtdylyUJa1HWYtNxxEBQAo9xOht7zPZVkErRzL9WvUzHUecQBkOLNl9qLRo2qe+bTqOCABS6KHE42Ht6rF8Ex7OrZ3uxWqxmk4k6rC44nJ+X2QjK+5HYsJ+NB1H+Dkp9FDy3adM1UdIskUx8IxBptMIryh2Hh5GlEeTniajdHFiMm0xRKSPWsC46MdZ1SKC+8+9jXBruOlIwks7XO25Kj+FJSl5tIhaDdRvZtLRc9f3jpFZTcFMRughorvlW9YkFGL1WLn+7CGm44h6Wp53B6c53UQ2WYDbI6sxitpJoYeIIeHz+CQqkqojXYkLjzMdR9TTEZ1Iq5xzORDuZv6q50zHEX5KCj0UHPianQkH0CjK839vOo04SUsLb+SsCg+v7n6HsvIC03GEH5JCDwFFK1/ivZhodNF5aFe86TjiJDmxQ/al5Fhg6uL7TccRfkgKPdjl7+H9/V9SbrFQmtfbdBpxijLL+nKpimFq7gYO5+4wHUf4GZnlEuScq8YxIzYGS2lLPHJ5uaDw54vGsGTZvUxYfD/TNv1frdvIbJbQJCP0YFZymIXfzSPbZqUk/xLTaYSPtEi/iBsjT2dexX7aODaajiP8iBR6ENNrX+etmAhaRzXDXSKLcAWTEZe+QoyG5NT3AW06jvATcsglWFWVsn7LVLYnRvJkhzt5MPN/P7vlIgmBLy6+FXenXcSLh1fQNXoB60p+fZES+R6HJhmhB6tNM3k7HBLs0Qw4fYDpNEHDn64cNKTPWJo4NeWpKwij0nQc4Qek0IORx82Pa1/hy8hIbmg3DIfNYTqRaABhYZE4cnqyN9xCr4TppuMIPyCHXILR9o+YThE2SzxD5DR/v9EQo/pthQM4N3Ete5J3kFiQQ75O8flriMAhI/RgozWFX41jfkwM/VtfQXJEsulEokEpCrOvJtdmpXvyf02HEYbJCD3Y7FvLeyW7KE9M4OZzbjGdRjSAY0f6+8oy6FSykMzEXNoe2c53rnaGkgnTZIQeZJyrxjMrLo6uqb/jrMSzTMcRjeT77JuoVIozU2cg0xhDV52FrpSaopQ6rJTadpz7lVJqvFJqt1Jqi1LqfN/HFF7J+54vspaSbbUw/NxbTacRjai4qhWtClqwKtZJD8dS03GEId6M0KcCl5/g/v7AmTUfI4D/nHoscVLWTuTtuFhaRJ3GRc0vMp1GNLJtOTcT7oHw1E8Jw2k6jjCgzkLXWi8H8k+wyVXAW7raGiBeKdXUVwGFl8ry2fLNbLaEhzHsnJuxKDmaFmrc7lji8zuxPsrK5dFzTMcRBvjif30zYN9Rt7NqvvYbSqkRSqlMpVRmTk6OD15a/GLDVKZH2om2RXD1GVebTiMM2Zk3mASnhf2pX5NIgek4opH5YpaLquVrtb4ro7WeBEwCyMjIkHdufMVVxaHMSXyeGMWNba8nyh7lF2cyCgO0HXdOX747bREDEv7LrCMPmE4kGpEvRuhZQIujbjcHDvjgeYW3vpnHHEsZHhRDzx5qOo0wbH9hb5pUOFifvJ+2lu9NxxGNyBeF/iFwc81sl25Aodb6oA+eV3ghfdQCNsz9B3NiYrm4xcU0j2luOpIwzsLhQ9eTbbPRNXkax5vG6E/r0gjf8Gba4ixgNXCWUipLKXWHUmqkUmpkzSafAHuA3cAbwL0Nllb8Rle1g70xuRRbFcPa32Q6jvATReXn0LQkmc8TKrjYvtJ0HNFI6jyGrrU+4e/wWmsN3OezRKJe7rB9zIS4ODwVaVz/72xARlui2p7s4USf/i+SU+YTdqAbVdhNRxINTOa2BbK874mN/JYfwmxU5vek9venRahyVTUhoeBsFsVauTbiPdNxRCOQQg9kaycyPS4GXJG4ijqaTiP80N6cGwjzWMhLXUeKTGMMelLogaq8gH1bZrE8MoLKgm6g5ddp8VvaHYUlrydrIsO5Jnaq6TiigUmhB6qN05gZaQUsOI90M51G+LHs/MuIrQpjfcpPuPatNx1HNCBZPjcQuV2UrJvEvIQ4nEUd0K5Y04mEP9M2Cg8Poqj5e8z9/M/ccNtKUL9+v+XYqYt7x1zZmAmFj8gIPRBt/5D5uoBSpanK72E6jQgAJcW/I6EsgQkcoXiTXK4uWEmhByDPmgnMjE+kQ3IHPBUt6n6AECj2Z9/IEYuVN9aMgapS04FEA5BCDzT71rMybxs/WeEmOZFI1IO7ogUDm17I9AjFvqVPmY4jGoAUeqBZM4Hp8QmkRiTTt1Vf02lEgLm/1zPYlJWX98yjpco2HUf4mBR6ICnYx+5dn7DaYWdou2HYLTJVUdRPamQqd7S/mc8jHQyNmWI6jvAxKfRAsu51ZsRGE24JY/CZg02nEQHqls73cZotmi+Sc7jI8rXpOMKHpNADRWUJBRvf5qOYaAa0GUi8I950IhGgHDYHf+n2GDvDw+iWMEMuVxdEpNADxaYZvBfuoRLNsHbDTKcRAe7S068guiyF2UmK4faPTMcRPiKFHgg8bpxrJjArIZFuTbtxZsKZphOJAKeUIvvQEAosVlTKUpqSZzqS8AEp9ECw81MWV+VwWHm4qZ1MVRS+4alshr2gA+/FRnJn1H9NxxE+IIUeAPTqV3k7MZlWMS3p1byX6TgiiOTnXIXVY2N1ShYXWraYjiNOkRS6v9u/kc3ZG9hqg2Htb8Ki5FsmfEe7oyjLuZy1EQ76x72FHZfpSOIUSDv4uzWv8XZ8IjH2GK5qc5XpNCIIlR+5kIjKON5OhttsH5qOI06BrLbozwr3c2DHhyxu3oRb2g4m0h5pOpEISlbyDg6hPP11HMlLaJ7d81erL8rKi4FDRuj+bO1EZsVEopSFG9vdaDqNCGLu8tbYCtszPT6KeyPkDdJAJSN0f1VZTOnGabzfNJG+rfqSFpX2y13Hrl0thC8UZF9DQvROlqccoN++dXzu6Qogo/UAIiN0f/X1dOaFeSjGzc3tbzadRoQA7Y6hNOcyVkVG0C9uBlGUm44k6klG6P7I7cK15jWmJybTObUDHVI6mE4kgkRdv91VHulBdPwaJiUf5o8lc3jBeWvjBBM+ISN0f7TjI5ZU5bBfubml/S2m04iQYuXIwSFkW20UJ6/nXLXHdCBRD1Lo/kZrWDWeaUkptIhpQe8WvU0nEiHGU9ESCs5nRlw0I6PewIrbdCThJSl0f/PjKjblbWOLDYa3H47VYjWdSISg4sMDsLrDmZVSwW3WT0zHEV6SQvc3q8YzLTGZ2LBYOZFImOOJpCj7arY4wmmZ+Klc3ShASKH7k8M72PvDF3zhsPGHs/4gJxIJo1xFnbGUpDMhMZqHwycBmvRRH//yIfyPFLo/+eoV3kpIwG6xy4lEwg8oig5dTwU2FqbmMNi6zHQgUQcpdH9RdJDcbe8yPzqKQWdcRXJEsulEQqCdSZTnXMqyqEh6xb1Lmqyb7te8KnSl1OVKqZ1Kqd1KqVG13N9bKVWolNpU8/GE76MGr/RRH/P6P//KzGgHTrRMVRR+pSq/F9aKVP6VFMXfwt8AtOlI4jjqPLFIKWUFJgD9gCxgvVLqQ631t8dsukJrPaABMga9WEq4xraEAbGpVBW1p/fz3wDf/Oo0azlmKcyxUnRgCJ7Wr/BV6n6u27+C9z0XmQ4lauHNCL0rsFtrvUdrXQXMBmT6hQ8Nty7ms1gb5VZNVb78RxH+x1N5GpW5F7MgOoo+cbNoQr7pSKIW3hR6M2DfUbezar52rO5Kqc1KqU+VUufU9kRKqRFKqUylVGZOTs5JxA1CVWUMs33GpLhEXKWn4ylvZTqRELWqzL0Ea0USY5OjeSp8YvVJcMKveFPoqpavHfud3Ai00lp3BF4BPqjtibTWk7TWGVrrjJSUlHoFDVqbZrA6xk2hTVOV19t0GiFOwEbRwaHkWm18mXoQMiebDiSO4U2hZwEtjrrdHDhw9AZa6yKtdUnN558AdqWUTNOoi9uJe9V4XotLxl3eDHfpmaYTCXFCnormVNQcelm8/BnI+950JHEUbwp9PXCmUqq1UioMGAL86jpVSqk0pZSq+bxrzfPK/Ka6bJnD565cDof9PDqv7ZchIfxLVW4fVHkTnk6IJnfuneB2mo4katRZ6FprF/BHYCGwHXhHa/2NUmqkUmpkzWaDgW1Kqc3AeGCI1nKA7YTcLjwrxvJGchPclSm4imt920EIP2Sl5MCNlNrCeMr5E3rZGNOBRA1lqnczMjJ0Zmamkdf2C1ve5YvP/sSfm6RQvv8GXEXnm04kRL08PTyPFzNf5PG8I9xw3TvQ6kLTkUKCUmqD1jqjtvvkTFETPB70ihd5PbkJLWNa4irqaDqREPV2U/ubuDCtKy8mJrDng7ug/IjpSCFPCt2E7R/yZclPbLd6uKvDXYAskSsCj0VZeLbXGCLCYng40k3VB/fKVEbDpNAbm8eDXvY8/0lJpXl0cwacLifXisCVEpnCM72eZ2eYnZdyVsPa101HCmlyTdHG9u08VpTs5dvoVJ7uMAKbRb4FIjAdvRzFvdcO5+3tb5Ox8ln6tegCzX5nMFnokhF6Y/K48Sx7nldT0vBUJfLAZKus0SKCwgO/e4DzEtvxRFI8+96/FcpkaQATpNAb07b3+bwsi+1WD5U5fZFj5yJY2K12Xrz4ZVRYFH+NcFL53u3gkWuRNjYp9MbiduFe9jwTUprQJu50XEWdTCcSwqeaRTfjuYteYHuYnWeKNqOX/MN0pJAjhd5Yvn6bBVXZ/GDx8MfOf0L+6kUw+fmydLdOKGVkh7uZHxPNnM2vw/YFpqOFFGmVxlBVRtWyMfw7vnrNljv/U2E6kRAN5p5O9/L703ryQlIiGxfcC4e2mo4UMqTQG8Pa/zDLUkquXVOZczmyZosIZhZl4bnfv0Cz6GY8kBxL1pyhUHLYdKyQIIXe0MryKVg1jteTknCVtJUVFUVIiA2L5dV+EynQDu6NdLFibH9wym+mDU0mQTe05WN5PdJCKZrKw1eYTiNEgzt6Kq41cjh7W05mRpNCur9/J7YbpoFFZnc1FBmhN6TcXfy08U1mx8VyzZnX4qlMM51IiEblLjuD8kPXsCoygqdzV6E/fUSWB2hAUugNaeHfGJuYiN0azn2d7jOdRggjnAVdqcy5hHkx0byy+x1Y9W/TkYKWFHpD2bWY5VlfsjTCzoiOd5MSKZfcE6GrKrcf151xHW/ExzFj3VhY/6bpSEFJjqE3BLeTyoWjGJOSSnpsK25pf4vpREIYpnis+2MUVOYzhqU4vnyC6+yR0OlG08GCiozQG8LqCUxxZbPPCo9e8DfsVrvpREIYZ7PY+Ofvx9Kz6YU8lZLEh4sfgq3vmY4VVKTQfS3/B/at+CeTExK4LP0yup/W3XQiIfxGmDWMly8ZxwVNuvB4ciIfLbwfNs0yHStoSKH7ktZ4FjzA40mx2G0RPJTxkOlEQvgdh83B+L4T6JKWwaMpicz54kHYMNV0rKAghe5LW99jVu56NoTbyfmpPxc8E8LXTBXiBNo9toTFX16Fp/gsnk1O5M3lj6O/fFGmNJ4iKXRfKc5m3+ejGJeYiKukLa7CWq/hKoT4mbZTmnUz7sIOjEuM5x9bJuBa8IAsu3sKpNB9QWtcH9zDY9E2rPZIKg5eh6zXIoQ3rJQdGEJVXi/mxMbwp6wFlM68ASoKTQcLSFLovrBuEq/lZ7LREUbOjwPRrjjTiYQIIBYqD19JxcGrWR0ZybDyb/hh8sWQu8t0sIAjhX6qDm9nxYpneSM+jqojXXAVdTadSIiA5CzoRvGPt7PXEs2QyCoWv30ZfDPPdKyAIoV+KsqPcHDOUEYnxaEqUqnMHmQ6kRABzV12JoU/PEBFZVMeSIzi2SUPUDb/XqgqNR0tIEihnyy3i+J3b+E+RwUuewTF+4eDlhOIhDhV2hVP4Y9/5JZ2w3knNobrc5aw6Y0esHeV6Wh+TwrdCz9fXuvoZUGrPn+MP5dt54ewcF6+ZDy6StZqEcJntI0Huz7M5Mum4Ipuws1Rbp7+aBiFH/4RygtMp/NbspbLcRxd3sdyr3iJx75/h3XRUTzX89mas0Fr3/5EzyOEOLEuaV2Ye90nvLZhHDN2zmZx7hLufaML13X9C/Yud4Isq/ErUuj19MxjI8g97QuWREfxwPn3M7DNQNORhAhqUfYoHur2KIPaXsfzKx/jH9YdTN02nutWjOebIwNY4OmJCxt7x1xpOqpxcsjFSwoPI+zvsrvFUpZGRlJ16EpuP+9O07GECBlnJZ7Ffwe+Q9lPt3LEncz4VBtb2yzg3tRHGGb/EMqPmI5onIzQvRBLCffEvMKHTXI5aHNQsf8PVBV3lsMpQtSDL/6/KKVwl55N9g8PY43eSXnip/w36TD2xFWUT+3KgMSO9Oh0O+Ft+oItzOs8wTK6V9qLtROUUpcD4wAr8KbWeswx96ua+68AyoBbtdYbT/ScGRkZOjPT/Fonx/umpo/6GIWHi+2raJo8nw/jbURVOcg5cAvu8tYmogohamEJP0Ba/FLsSTvI104cHg8XVLnpEduGTi0u4syzrsGWfCaoX5+9fbwfMP5e7kqpDVrrWtcWqbPQlVJW4DugH5AFrAeGaq2/PWqbK4A/UV3oFwDjtNYXnOh5T6XQffmT9dhvajjltAr7jmaOHYTHbmRdNDiVIi6/PVmHh4A+8U99IYQZu567lLX7VrB8xzssz97Afl0BQITHQ+sqN3FVEVzQtA1psS1IjT+dxz/Op9idQJE7iQodiRM7dS3ZcSp946veOlGhe3PIpSuwW2u9p+bJZgNXAd8etc1VwFu6+qfDGqVUvFKqqdb64EmnNuCi1HFsSTzAQaU4CES6IbXgdHbnD6K4qqnpeEKIE7Bb7PRsdQk9W13CaK05ULKfzXsWMnHp+5SG57A/soLVpTuhdCccBE7/32MdQJTW2DQoNAo4uzCZ5YceNrQ3J8ebEfpg4HKt9Z01t4cDF2it/3jUNguAMVrrlTW3vwAe0VpnHvNcI4ARNTfPAnb6akd8KBnINR3Ch2R//Fcw7QvI/jSWVlrrWk988WaEXtvvIMf+FPBmG7TWk4BJXrymMUqpzOP9OhOIZH/8VzDtC8j++ANvpi1mAS2Out0cOHAS2wghhGhA3hT6euBMpVRrpVQYMAT48JhtPgRuVtW6AYWBdvxcCCECXZ2HXLTWLqXUH4GFVE9bnKK1/kYpNbLm/onAJ1TPcNlN9bTF2xoucoPz60NCJ0H2x38F076A7I9xXs1DF0II4f/k1H8hhAgSUuhCCBEkQrbQlVKXK6V2KqV2K6VG1XK/UkqNr7l/i1LqfBM5veXF/gyr2Y8tSqmvlFIdTeT0Rl37ctR2XZRS7ppzJfyWN/ujlOqtlNqklPpGKfVlY2esDy/+rcUppT5SSm2u2R+/fU9NKTVFKXVYKbXtOPcHVA+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SnoOrder IDDate of placing orderOrder Dispatch dateLogistics TypeNameSegmentCountryCityState...DiscountProfitUnnamed: 20log10000Total SalesMonthQuarterUnnamed: 25Unnamed: 26Unnamed: 27
0740CA-2014-1123262014-01-042014-01-08Standard ClassPhillina OberHome OfficeUnited StatesNapervilleIllinois...0.24.271710.26782338127.933JanQ139360.06045NaNNaN
1741CA-2014-1123262014-01-042014-01-08Standard ClassPhillina OberHome OfficeUnited StatesNapervilleIllinois...0.2-64.774810.60893621452.645FebNaNNaNNaNNaN
2742CA-2014-1123262014-01-042014-01-08Standard ClassPhillina OberHome OfficeUnited StatesNapervilleIllinois...0.8-5.487010.13725197859.6638MarNaNNaNNaNNaN
31760CA-2014-1418172014-01-052014-01-12Standard ClassMick BrownConsumerUnited StatesPhiladelphiaPennsylvania...0.24.884010.32270981724.5361AprQ255751.25475NaNNaN
4593CA-2014-1354052014-01-092014-01-13Standard ClassMelanie SeiteConsumerUnited StatesLaredoTexas...0.21.168010.24263370289.3068MayNaNNaNNaNNaN
..................................................................
4995907CA-2017-1432592017-12-302018-01-03Standard ClassPatrick O'DonnellConsumerUnited StatesNew York CityNew York...0.212.1176120.627346NaNNaNNaNNaNNaNNaN
4996908CA-2017-1432592017-12-302018-01-03Standard ClassPatrick O'DonnellConsumerUnited StatesNew York CityNew York...0.02.7279120.489677NaNNaNNaNNaNNaNNaN
4997909CA-2017-1432592017-12-302018-01-03Standard ClassPatrick O'DonnellConsumerUnited StatesNew York CityNew York...0.219.7910120.430609NaNNaNNaNNaNNaNNaN
49981297CA-2017-1154272017-12-302018-01-03Standard ClassErica BernCorporateUnited StatesFairfieldCalifornia...0.24.5188120.285785NaNNaNNaNNaNNaNNaN
49991298CA-2017-1154272017-12-302018-01-03Standard ClassErica BernCorporateUnited StatesFairfieldCalifornia...0.26.4750120.329097NaNNaNNaNNaNNaNNaN
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Discount Profit Unnamed: 20 \\\n", + "0 Naperville Illinois ... 0.2 4.2717 1 \n", + "1 Naperville Illinois ... 0.2 -64.7748 1 \n", + "2 Naperville Illinois ... 0.8 -5.4870 1 \n", + "3 Philadelphia Pennsylvania ... 0.2 4.8840 1 \n", + "4 Laredo Texas ... 0.2 1.1680 1 \n", + "... ... ... ... ... ... ... \n", + "4995 New York City New York ... 0.2 12.1176 12 \n", + "4996 New York City New York ... 0.0 2.7279 12 \n", + "4997 New York City New York ... 0.2 19.7910 12 \n", + "4998 Fairfield California ... 0.2 4.5188 12 \n", + "4999 Fairfield California ... 0.2 6.4750 12 \n", + "\n", + " log10000 Total Sales Month Quarter Unnamed: 25 Unnamed: 26 \\\n", + "0 0.267823 38127.933 Jan Q1 39360.06045 NaN \n", + "1 0.608936 21452.645 Feb NaN NaN NaN \n", + "2 0.137251 97859.6638 Mar NaN NaN NaN \n", + "3 0.322709 81724.5361 Apr Q2 55751.25475 NaN \n", + "4 0.242633 70289.3068 May NaN NaN NaN \n", + "... ... ... ... ... ... ... \n", + "4995 0.627346 NaN NaN NaN NaN NaN \n", + "4996 0.489677 NaN NaN 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--- Statistics/Week 9 Statistics.ipynb | 284 ----------------------------- 1 file changed, 284 deletions(-) delete mode 100644 Statistics/Week 9 Statistics.ipynb diff --git a/Statistics/Week 9 Statistics.ipynb b/Statistics/Week 9 Statistics.ipynb deleted file mode 100644 index fda0f4d..0000000 --- a/Statistics/Week 9 Statistics.ipynb +++ /dev/null @@ -1,284 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "300 3.8933333333333335\n" - ] - } - ], - "source": [ - "'''\n", - "Problem 1\n", - "Fitting a Poisson distribution for a number of vehicles (n)\n", - "making a right turn at an intersection in a 3-min interval.\n", - "'''\n", - "\n", - "import numpy as np\n", - "\n", - "freq = np.array([14,30,36,68,43,43,30,14,10,6,4,1,1])\n", - "num = np.arange(0,13)\n", - "\n", - "n = np.sum(freq)\n", - "sample_mean = np.sum(num*freq)/n\n", - "print(n,sample_mean)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 6.1131925 23.80069615 46.33202183 60.12866833 58.52523717 45.57165135\n", - " 29.57093821 16.4470742 8.00424278 3.46257614 1.34809631 0.47714439\n", - " 0.15480685]\n" - ] - } - ], - "source": [ - "import scipy.stats as st\n", - "\n", - "poiss_fit = st.poisson.pmf(num, sample_mean)\n", - "print(poiss_fit*n)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "2.2793176366818404\n" - ] - } - ], - "source": [ - "#Sample Variance Calculation \n", - "v = np.sum(freq*((num - sample_mean)**2))/(n)\n", - "print(np.sqrt(v))" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.2579243321097385 -0.25792433210973853\n" - ] - } - ], - "source": [ - "#Finding inverse cdf\n", - "\n", - "l1 = st.norm.ppf(0.975,loc=0,scale=np.sqrt(v/300))\n", - "l2 = st.norm.ppf(0.025,loc=0,scale=np.sqrt(v/300))\n", - "\n", - "print(l1,l2)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "3.635409001223595 4.151257665443072\n" - ] - } - ], - "source": [ - "#Confidence Interval:\n", - "\n", - "print(sample_mean - l1 , sample_mean - l2)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "130 0.3581267217630854\n" - ] - } - ], - "source": [ - "'''\n", - "Problem 2\n", - "Fitting a geometric distribution for number of hops(n) between\n", - "flight of birds\n", - "'''\n", - "\n", - "import numpy as np\n", - "import scipy.stats as st\n", - "\n", - "num = np.arange(1,13)\n", - "freq = np.array([48,31,20,9,6,5,4,2,1,1,2,1])\n", - "\n", - "n = np.sum(freq)\n", - "phat = n/np.sum(freq*num)\n", - "print(n, phat)" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.001924125127040266\n", - "0.025348771614737402\n" - ] - } - ], - "source": [ - "#Finding E[phat] using BOOTSTRAP Method:\n", - "\n", - "N = 10000\n", - "phat_bootstrap = np.zeros(N)\n", - "for i in range(N):\n", - " xi = st.geom.rvs(phat, size=n)\n", - " phat_bootstrap[i] = n/np.sum(xi)\n", - "\n", - "bias_bootstrap = np.average(phat_bootstrap) - phat\n", - "print(bias_bootstrap)\n", - "\n", - "#Finding variance using BOOTSTRAP Method:\n", - "\n", - "var_bootstrap = np.var(phat_bootstrap, ddof = 1)\n", - "print(np.sqrt(var_bootstrap))" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.006357459240353004 -0.002357459240353005\n" - ] - } - ], - "source": [ - "#Finding Inverse CDF\n", - "\n", - "l1 = st.norm.ppf(0.975,loc=0.002,scale=np.sqrt(var_bootstrap/n))\n", - "l2 = st.norm.ppf(0.025,loc=0.002,scale=np.sqrt(var_bootstrap/n))\n", - "\n", - "print(l1,l2)" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.3517692625227324 0.36048418100343843\n" - ] - } - ], - "source": [ - "#Confidence Interval\n", - "\n", - "print(phat-l1,phat-l2)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.9500268556941498\n" - ] - } - ], - "source": [ - "'''\n", - "Problem 3\n", - "In a new machine, suppose that out of 10 produced items,\n", - "no items was found to be defective. Estimate the probability \n", - "of defective items produced by the new machine? Prior Data:\n", - "avg. fraction of defective items = 10% and actual fraction was\n", - "between 5% and 15% in 95% of the cases.\n", - "'''\n", - "\n", - "import numpy as np\n", - "import scipy.stats as st\n", - "\n", - "#a = alpha\n", - "#For a particular alpha we are trying to find what value will\n", - "#make the last condition to be 0.95\n", - "fb = lambda a: (st.beta.cdf(0.15,a,9*a) - st.beta.cdf(0.05,a,9*a))\n", - "print(fb(13.3))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "interpreter": { - "hash": "000b55af9c8c6e0b177305578cfd5e8b3858975f719edc1b51e24deccc4249ae" - }, - "kernelspec": { - "display_name": "Python 3.9.7 64-bit ('minimal_ds': conda)", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.7" - }, - "orig_nbformat": 4 - }, - "nbformat": 4, - "nbformat_minor": 2 -} From 777d944c0470b7b2c641e530e980f0c230ade598 Mon Sep 17 00:00:00 2001 From: bala35210 Date: Sun, 16 Jan 2022 18:24:57 +0530 Subject: [PATCH 5/7] Create README --- Statistics/README | 11 +++++++++++ 1 file changed, 11 insertions(+) create mode 100644 Statistics/README diff --git a/Statistics/README b/Statistics/README new file mode 100644 index 0000000..78a5236 --- /dev/null +++ b/Statistics/README @@ -0,0 +1,11 @@ +I've taken a sales dataset from a reputed source and tried to fit distributions such as normal, beta and assess if its a good fit or not. +Two approaches were taken to arrive at the results: + +Approach 1: Calculate the theoretical and practical CDF's and compare it. Here, we considered two such CDF's i.e., Normal CDF and Beta CDF with suitable parameters. + -> Tools Used: Microsoft Excel + -> The Beta Fit and Normal Fit CDF graphs can be looked at their respective *.xlsx files. + -> Futhur explanations can be found in the "Calculations" pdf document. + +Approach 2: Estimate the Beta distribution parameters using "Method of Moments(MM)" and "Method of Maximum Likelihood(ML)" and compare the fit with its respective histogram. + -> Tools Used: Python and its packages such as 'scipy.stats','numpy','pandas','matplotlib'. + From 3dc8a8ed172bdf6ed5cba5fa0d1cf4a8e3beaa73 Mon Sep 17 00:00:00 2001 From: bala35210 Date: Sun, 16 Jan 2022 18:25:49 +0530 Subject: [PATCH 6/7] Some useful Instructions From 4444647d3fad11c77a91652d31461fc713382cbc Mon Sep 17 00:00:00 2001 From: bala35210 Date: Sun, 16 Jan 2022 18:48:50 +0530 Subject: [PATCH 7/7] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index e4a98e6..a5dd78e 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,5 @@ - šŸ‘‹ Hi, I’m @bala35210 -- šŸ‘€ I’m interested in data analyst, scientist and ML/AI engineer. +- šŸ‘€ I’m interested in data analyst, scientist and ML/AI. - 🌱 I’m currently learning Machine Learning and Data Analytics. - šŸ’žļø I’m looking to collaborate on data analyst projects. - šŸ“« You can reach me @ Linkedin: https://www.linkedin.com/in/balakumaran-selvaraji-9b4a1b105/

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