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@TimOliverMaier
Last active December 9, 2022 11:45
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scipy stats scale
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import scipy as sp\n",
"plt.style.use(\"bmh\")"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook shall illustrate [this](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.html#:~:text=Note%20that%20above%20we%20defined%20a%20standard%20normal%20distribution%2C%20with%20zero%20mean%20and%20unit%20variance.%20Shifting%20and%20scaling%20of%20the%20distribution%20can%20be%20done%20by%20using%20loc%20and%20scale%20parameters%3A%20gaussian.pdf(x%2C%20loc%2C%20scale)%20essentially%20computes%20y%20%3D%20(x%20%2D%20loc)%20/%20scale%20and%20gaussian._pdf(y)%20/%20scale.) statement from the scipy documentation:\n",
"\n",
"\"Note that above we defined a standard normal distribution, with zero mean and unit variance. Shifting and scaling of the distribution can be done by using loc and scale parameters: gaussian.pdf(x, loc, scale) essentially computes y = (x - loc) / scale and gaussian._pdf(y) / scale.\""
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"x = np.arange(-2000,2000+1)/100"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def _pdf(x):\n",
" return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)\n",
"def pdf(x,loc=0,scale=1):\n",
" return _pdf((x-loc)/scale)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"p = pdf(x,10,2)\n",
"p_s =pdf(x,10,2)/2"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x,p)\n",
"plt.plot(x,p_s)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Integral approximation for blue function : 1.9999994340994809\n",
"Integral approximation of red function : 0.9999997170497404\n"
]
}
],
"source": [
"print(f\"Integral approximation for blue function : {p.sum()*0.01}\")\n",
"print(f\"Integral approximation of red function : {p_s.sum()*0.01}\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "pymc_dev",
"language": "python",
"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": "3.10.6"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "e72a8d8ce8364635d68c11ed264ecd033ec926576ac60b4957a81f7389674ed5"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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