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Confidence Interval Notebooks #15

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Confidence Interval Notebooks #15

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ed2e7e2
initial confidence interval notebook with a widget
valentina-s Oct 14, 2024
09a43d9
first version of confidence intervals
valentina-s Oct 18, 2024
5d23025
moving confidence intervals
valentina-s Oct 18, 2024
84726a6
bootstrap
valentina-s Oct 21, 2024
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162 changes: 162 additions & 0 deletions boat_tutorials/CLT.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Central Limit Theorem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"IID Case"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy as sp\n",
"import math\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"scale = 1\n",
"N = 1000\n",
"x = np.random.exponential(scale, N)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([58., 60., 74., 50., 53., 40., 46., 41., 33., 35., 36., 36., 30.,\n",
" 29., 20., 21., 15., 18., 21., 17., 13., 18., 21., 13., 17., 14.,\n",
" 8., 7., 10., 11., 11., 8., 11., 8., 12., 4., 4., 6., 4.,\n",
" 3., 7., 6., 1., 0., 5., 4., 4., 2., 0., 2., 3., 0.,\n",
" 5., 2., 1., 1., 2., 0., 1., 1., 1., 2., 1., 2., 0.,\n",
" 1., 0., 1., 0., 0., 1., 0., 1., 0., 0., 0., 1., 1.,\n",
" 0., 0., 1., 0., 0., 0., 0., 1., 0., 0., 1., 0., 0.,\n",
" 1., 0., 0., 0., 0., 0., 0., 0., 1.]),\n",
" array([3.31894143e-03, 7.01172415e-02, 1.36915542e-01, 2.03713842e-01,\n",
" 2.70512142e-01, 3.37310442e-01, 4.04108742e-01, 4.70907042e-01,\n",
" 5.37705342e-01, 6.04503642e-01, 6.71301942e-01, 7.38100242e-01,\n",
" 8.04898542e-01, 8.71696842e-01, 9.38495142e-01, 1.00529344e+00,\n",
" 1.07209174e+00, 1.13889004e+00, 1.20568834e+00, 1.27248664e+00,\n",
" 1.33928494e+00, 1.40608324e+00, 1.47288154e+00, 1.53967984e+00,\n",
" 1.60647814e+00, 1.67327644e+00, 1.74007474e+00, 1.80687304e+00,\n",
" 1.87367134e+00, 1.94046964e+00, 2.00726794e+00, 2.07406624e+00,\n",
" 2.14086454e+00, 2.20766284e+00, 2.27446114e+00, 2.34125944e+00,\n",
" 2.40805774e+00, 2.47485604e+00, 2.54165434e+00, 2.60845264e+00,\n",
" 2.67525094e+00, 2.74204924e+00, 2.80884754e+00, 2.87564584e+00,\n",
" 2.94244414e+00, 3.00924244e+00, 3.07604074e+00, 3.14283905e+00,\n",
" 3.20963735e+00, 3.27643565e+00, 3.34323395e+00, 3.41003225e+00,\n",
" 3.47683055e+00, 3.54362885e+00, 3.61042715e+00, 3.67722545e+00,\n",
" 3.74402375e+00, 3.81082205e+00, 3.87762035e+00, 3.94441865e+00,\n",
" 4.01121695e+00, 4.07801525e+00, 4.14481355e+00, 4.21161185e+00,\n",
" 4.27841015e+00, 4.34520845e+00, 4.41200675e+00, 4.47880505e+00,\n",
" 4.54560335e+00, 4.61240165e+00, 4.67919995e+00, 4.74599825e+00,\n",
" 4.81279655e+00, 4.87959485e+00, 4.94639315e+00, 5.01319145e+00,\n",
" 5.07998975e+00, 5.14678805e+00, 5.21358635e+00, 5.28038465e+00,\n",
" 5.34718295e+00, 5.41398125e+00, 5.48077955e+00, 5.54757785e+00,\n",
" 5.61437615e+00, 5.68117445e+00, 5.74797275e+00, 5.81477105e+00,\n",
" 5.88156935e+00, 5.94836765e+00, 6.01516595e+00, 6.08196425e+00,\n",
" 6.14876255e+00, 6.21556085e+00, 6.28235915e+00, 6.34915745e+00,\n",
" 6.41595575e+00, 6.48275405e+00, 6.54955235e+00, 6.61635065e+00,\n",
" 6.68314895e+00]),\n",
" <BarContainer object of 100 artists>)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(x, 100)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"x = np.random.exponential(scale, N)\n",
"mean(x)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Cauchy example\n",
"\n",
"# Diverging variances"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
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