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gmartin6
simulating_quartets
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42f0a856
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42f0a856
authored
4 years ago
by
Großhauser
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scaling_behavior
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Scaling_Behavior.ipynb
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42f0a856
{
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"import scipy.stats as stats\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [],
"source": [
"def scale_x(x,f):\n",
" return [f*i for i in x ]\n",
"\n",
"\n",
"x = np.linspace(0,10,1000)\n",
"y1 = stats.gamma.pdf(x, a=2, scale=1)\n",
"y2 = stats.gamma.pdf(scale_x(x,0.1), a=2, scale=0.1)\n",
"y3 = stats.gamma.pdf(scale_x(x,10), a=2, scale=10)\n",
"y4 = stats.gamma.pdf(scale_x(x,100), a=2, scale=100)\n",
"y5 = stats.gamma.pdf(scale_x(x,1000), a=2, scale=1000)\n"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x,y1,c=\"b\",label=\"orig\")\n",
"plt.plot(x,y2*0.1,c=\"r\",label=\"0.1\")\n",
"plt.plot(x,y3*10,c=\"g\",label=\"10\")\n",
"plt.plot(x,y4*100,label=\"100\")\n",
"plt.plot(x,y5*1000,label=\"1000\")\n",
"\n",
"plt.ylim((0,1))\n",
"plt.xlim((0,10))\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1002.0"
]
},
"execution_count": 99,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"stats.gamma.mean(2,1000)"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1004.4725473220625 10130.722996043432 103046.80840506486\n"
]
}
],
"source": [
"s1 = sum(stats.gamma(a=1, scale=1).rvs() for _ in range(1000))\n",
"s2 = sum(stats.gamma(a=1, scale=10).rvs() for _ in range(1000))\n",
"s3 = sum(stats.gamma(a=1, scale=100).rvs() for _ in range(1000))\n",
"\n",
"print(s1,s2,s3)"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.03030884290065232"
]
},
"execution_count": 73,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"stats.gamma(a=1, scale=0.1).rvs()"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.009425970781589568"
]
},
"execution_count": 86,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"min(stats.gamma(a=1, scale=10).rvs() for _ in range(1000))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
%% Cell type:code id: tags:
```
python
import
scipy.stats
as
stats
import
numpy
as
np
import
matplotlib.pyplot
as
plt
```
%% Cell type:code id: tags:
```
python
def
scale_x
(
x
,
f
):
return
[
f
*
i
for
i
in
x
]
x
=
np
.
linspace
(
0
,
10
,
1000
)
y1
=
stats
.
gamma
.
pdf
(
x
,
a
=
2
,
scale
=
1
)
y2
=
stats
.
gamma
.
pdf
(
scale_x
(
x
,
0.1
),
a
=
2
,
scale
=
0.1
)
y3
=
stats
.
gamma
.
pdf
(
scale_x
(
x
,
10
),
a
=
2
,
scale
=
10
)
y4
=
stats
.
gamma
.
pdf
(
scale_x
(
x
,
100
),
a
=
2
,
scale
=
100
)
y5
=
stats
.
gamma
.
pdf
(
scale_x
(
x
,
1000
),
a
=
2
,
scale
=
1000
)
```
%% Cell type:code id: tags:
```
python
plt
.
plot
(
x
,
y1
,
c
=
"
b
"
,
label
=
"
orig
"
)
plt
.
plot
(
x
,
y2
*
0.1
,
c
=
"
r
"
,
label
=
"
0.1
"
)
plt
.
plot
(
x
,
y3
*
10
,
c
=
"
g
"
,
label
=
"
10
"
)
plt
.
plot
(
x
,
y4
*
100
,
label
=
"
100
"
)
plt
.
plot
(
x
,
y5
*
1000
,
label
=
"
1000
"
)
plt
.
ylim
((
0
,
1
))
plt
.
xlim
((
0
,
10
))
plt
.
legend
()
plt
.
show
()
```
%% Output
%% Cell type:code id: tags:
```
python
stats
.
gamma
.
mean
(
2
,
1000
)
```
%% Output
1002.0
%% Cell type:code id: tags:
```
python
s1
=
sum
(
stats
.
gamma
(
a
=
1
,
scale
=
1
).
rvs
()
for
_
in
range
(
1000
))
s2
=
sum
(
stats
.
gamma
(
a
=
1
,
scale
=
10
).
rvs
()
for
_
in
range
(
1000
))
s3
=
sum
(
stats
.
gamma
(
a
=
1
,
scale
=
100
).
rvs
()
for
_
in
range
(
1000
))
print
(
s1
,
s2
,
s3
)
```
%% Output
1004.4725473220625 10130.722996043432 103046.80840506486
%% Cell type:code id: tags:
```
python
stats
.
gamma
(
a
=
1
,
scale
=
0.1
).
rvs
()
```
%% Output
0.03030884290065232
%% Cell type:code id: tags:
```
python
min
(
stats
.
gamma
(
a
=
1
,
scale
=
10
).
rvs
()
for
_
in
range
(
1000
))
```
%% Output
0.009425970781589568
%% Cell type:code id: tags:
```
python
```
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