In [26]:
np.random.seed(0)
x = np.random.normal(size=100)
x
Out[26]:
array([ 1.76405235, 0.40015721, 0.97873798, 2.2408932 , 1.86755799,
-0.97727788, 0.95008842, -0.15135721, -0.10321885, 0.4105985 ,
0.14404357, 1.45427351, 0.76103773, 0.12167502, 0.44386323,
0.33367433, 1.49407907, -0.20515826, 0.3130677 , -0.85409574,
-2.55298982, 0.6536186 , 0.8644362 , -0.74216502, 2.26975462,
-1.45436567, 0.04575852, -0.18718385, 1.53277921, 1.46935877,
0.15494743, 0.37816252, -0.88778575, -1.98079647, -0.34791215,
0.15634897, 1.23029068, 1.20237985, -0.38732682, -0.30230275,
-1.04855297, -1.42001794, -1.70627019, 1.9507754 , -0.50965218,
-0.4380743 , -1.25279536, 0.77749036, -1.61389785, -0.21274028,
-0.89546656, 0.3869025 , -0.51080514, -1.18063218, -0.02818223,
0.42833187, 0.06651722, 0.3024719 , -0.63432209, -0.36274117,
-0.67246045, -0.35955316, -0.81314628, -1.7262826 , 0.17742614,
-0.40178094, -1.63019835, 0.46278226, -0.90729836, 0.0519454 ,
0.72909056, 0.12898291, 1.13940068, -1.23482582, 0.40234164,
-0.68481009, -0.87079715, -0.57884966, -0.31155253, 0.05616534,
-1.16514984, 0.90082649, 0.46566244, -1.53624369, 1.48825219,
1.89588918, 1.17877957, -0.17992484, -1.07075262, 1.05445173,
-0.40317695, 1.22244507, 0.20827498, 0.97663904, 0.3563664 ,
0.70657317, 0.01050002, 1.78587049, 0.12691209, 0.40198936])
In [33]:
sp.stats.describe(x)
Out[33]:
DescribeResult(nobs=100, minmax=(-2.5529898158340787, 2.2697546239876076), mean=0.059808015534484997, variance=1.0260874941564961, skewness=0.005171839713550013, kurtosis=-0.3783545566331328)
In [34]:
pd.Series(x).describe()
Out[34]:
count 100.000000
mean 0.059808
std 1.012960
min -2.552990
25% -0.643857
50% 0.094096
75% 0.737077
max 2.269755
dtype: float64
In [36]:
n, bins, patches = plt.hist(x, bins=100)
In [37]:
n
Out[37]:
array([ 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.,
0., 0., 0., 0., 2., 0., 2., 0., 1., 1., 1., 0., 0.,
1., 1., 2., 0., 1., 1., 1., 0., 4., 1., 1., 1., 2.,
1., 1., 0., 2., 1., 3., 3., 2., 0., 2., 3., 1., 0.,
1., 2., 3., 4., 3., 1., 0., 3., 3., 5., 3., 0., 0.,
0., 1., 1., 2., 1., 1., 1., 1., 2., 1., 0., 1., 2.,
2., 0., 0., 0., 0., 4., 1., 0., 0., 0., 0., 2., 0.,
1., 1., 1., 0., 0., 0., 0., 0., 2.])
In [38]:
bins
Out[38]:
array([-2.55298982, -2.50476237, -2.45653493, -2.40830748, -2.36008004,
-2.31185259, -2.26362515, -2.21539771, -2.16717026, -2.11894282,
-2.07071537, -2.02248793, -1.97426048, -1.92603304, -1.87780559,
-1.82957815, -1.78135071, -1.73312326, -1.68489582, -1.63666837,
-1.58844093, -1.54021348, -1.49198604, -1.44375859, -1.39553115,
-1.34730371, -1.29907626, -1.25084882, -1.20262137, -1.15439393,
-1.10616648, -1.05793904, -1.0097116 , -0.96148415, -0.91325671,
-0.86502926, -0.81680182, -0.76857437, -0.72034693, -0.67211948,
-0.62389204, -0.5756646 , -0.52743715, -0.47920971, -0.43098226,
-0.38275482, -0.33452737, -0.28629993, -0.23807248, -0.18984504,
-0.1416176 , -0.09339015, -0.04516271, 0.00306474, 0.05129218,
0.09951963, 0.14774707, 0.19597451, 0.24420196, 0.2924294 ,
0.34065685, 0.38888429, 0.43711174, 0.48533918, 0.53356663,
0.58179407, 0.63002151, 0.67824896, 0.7264764 , 0.77470385,
0.82293129, 0.87115874, 0.91938618, 0.96761363, 1.01584107,
1.06406851, 1.11229596, 1.1605234 , 1.20875085, 1.25697829,
1.30520574, 1.35343318, 1.40166062, 1.44988807, 1.49811551,
1.54634296, 1.5945704 , 1.64279785, 1.69102529, 1.73925274,
1.78748018, 1.83570762, 1.88393507, 1.93216251, 1.98038996,
2.0286174 , 2.07684485, 2.12507229, 2.17329974, 2.22152718,
2.26975462])
In [39]:
sns.distplot(x, rug=True)
Out[39]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f2b54987b50>
In [42]:
np.random.seed(0)
tips = sns.load_dataset("tips")
sns.jointplot(x="total_bill", y= "tip", data = tips)
Out[42]:
<seaborn.axisgrid.JointGrid at 0x7f2b545d3d90>
In [55]:
iris = sns.load_dataset("iris")
sns.jointplot("sepal_width", "petal_length", data = iris, kind="kde", space = 0,color = 'g', grid=False)
Out[55]:
<seaborn.axisgrid.JointGrid at 0x7f2b4cd5dbd0>
In [56]:
sns.pairplot(iris, hue="species", markers=['o','s','D'], size=2)
Out[56]:
<seaborn.axisgrid.PairGrid at 0x7f2b4cad0cd0>
In [57]:
flights = sns.load_dataset("flights")
flights = flights.pivot("month", "year", "passengers")
In [59]:
sns.heatmap(flights, annot=True, fmt='d', linewidths=1)
Out[59]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f2b3b99c310>
In [62]:
titanic = sns.load_dataset('titanic')
sns.factorplot(x="age", y="embark_town", hue="sex", row="class", data=titanic[titanic.embark_town.notnull()],
orient="h", size=2, aspect=3.5, palette='Set3', kind='violin', split=True, cut=0, bw=.2)
Out[62]:
<seaborn.axisgrid.FacetGrid at 0x7f2b3b77f910>
In [66]:
sp.random.seed(0)
x = sp.random.normal(size=1000)
In [68]:
ns, bins, ps = plt.hist(x, bins=10)
In [71]:
pd.DataFrame([bins, ns/1000])
Out[71]:
0
1
2
3
4
5
6
7
8
9
10
0
-3.046143
-2.465593
-1.885043
-1.304494
-0.723944
-0.143394
0.437156
1.017706
1.598255
2.178805
2.759355
1
0.009000
0.020000
0.070000
0.146000
0.217000
0.239000
0.160000
0.086000
0.038000
0.015000
NaN
In [74]:
x = np.linspace(-3,3,100)
y = sp.stats.norm.pdf(x)
plt.plot(x,y)
Out[74]:
[<matplotlib.lines.Line2D at 0x7f2b3b0ef050>]
In [81]:
tt = np.linspace(-100, 500, 100)
F = tt / 360
F[tt < 0] = 0
F[tt > 360] = 1
plt.plot(tt,F)
plt.ylim(-0.1, 1.1)
plt.xticks([0,180,360])
plt.title("Cumulative Distribution Function");
plt.xlabel("$x$ (deg.)");
plt.ylabel("$F(x)$");
Out[81]:
<matplotlib.text.Text at 0x7f2b3ae0ac50>
In [83]:
t= np.linspace(-100, 500, 1000)
t
Out[83]:
array([ -1.00000000e+02, -9.93993994e+01, -9.87987988e+01,
-9.81981982e+01, -9.75975976e+01, -9.69969970e+01,
-9.63963964e+01, -9.57957958e+01, -9.51951952e+01,
-9.45945946e+01, -9.39939940e+01, -9.33933934e+01,
-9.27927928e+01, -9.21921922e+01, -9.15915916e+01,
-9.09909910e+01, -9.03903904e+01, -8.97897898e+01,
-8.91891892e+01, -8.85885886e+01, -8.79879880e+01,
-8.73873874e+01, -8.67867868e+01, -8.61861862e+01,
-8.55855856e+01, -8.49849850e+01, -8.43843844e+01,
-8.37837838e+01, -8.31831832e+01, -8.25825826e+01,
-8.19819820e+01, -8.13813814e+01, -8.07807808e+01,
-8.01801802e+01, -7.95795796e+01, -7.89789790e+01,
-7.83783784e+01, -7.77777778e+01, -7.71771772e+01,
-7.65765766e+01, -7.59759760e+01, -7.53753754e+01,
-7.47747748e+01, -7.41741742e+01, -7.35735736e+01,
-7.29729730e+01, -7.23723724e+01, -7.17717718e+01,
-7.11711712e+01, -7.05705706e+01, -6.99699700e+01,
-6.93693694e+01, -6.87687688e+01, -6.81681682e+01,
-6.75675676e+01, -6.69669670e+01, -6.63663664e+01,
-6.57657658e+01, -6.51651652e+01, -6.45645646e+01,
-6.39639640e+01, -6.33633634e+01, -6.27627628e+01,
-6.21621622e+01, -6.15615616e+01, -6.09609610e+01,
-6.03603604e+01, -5.97597598e+01, -5.91591592e+01,
-5.85585586e+01, -5.79579580e+01, -5.73573574e+01,
-5.67567568e+01, -5.61561562e+01, -5.55555556e+01,
-5.49549550e+01, -5.43543544e+01, -5.37537538e+01,
-5.31531532e+01, -5.25525526e+01, -5.19519520e+01,
-5.13513514e+01, -5.07507508e+01, -5.01501502e+01,
-4.95495495e+01, -4.89489489e+01, -4.83483483e+01,
-4.77477477e+01, -4.71471471e+01, -4.65465465e+01,
-4.59459459e+01, -4.53453453e+01, -4.47447447e+01,
-4.41441441e+01, -4.35435435e+01, -4.29429429e+01,
-4.23423423e+01, -4.17417417e+01, -4.11411411e+01,
-4.05405405e+01, -3.99399399e+01, -3.93393393e+01,
-3.87387387e+01, -3.81381381e+01, -3.75375375e+01,
-3.69369369e+01, -3.63363363e+01, -3.57357357e+01,
-3.51351351e+01, -3.45345345e+01, -3.39339339e+01,
-3.33333333e+01, -3.27327327e+01, -3.21321321e+01,
-3.15315315e+01, -3.09309309e+01, -3.03303303e+01,
-2.97297297e+01, -2.91291291e+01, -2.85285285e+01,
-2.79279279e+01, -2.73273273e+01, -2.67267267e+01,
-2.61261261e+01, -2.55255255e+01, -2.49249249e+01,
-2.43243243e+01, -2.37237237e+01, -2.31231231e+01,
-2.25225225e+01, -2.19219219e+01, -2.13213213e+01,
-2.07207207e+01, -2.01201201e+01, -1.95195195e+01,
-1.89189189e+01, -1.83183183e+01, -1.77177177e+01,
-1.71171171e+01, -1.65165165e+01, -1.59159159e+01,
-1.53153153e+01, -1.47147147e+01, -1.41141141e+01,
-1.35135135e+01, -1.29129129e+01, -1.23123123e+01,
-1.17117117e+01, -1.11111111e+01, -1.05105105e+01,
-9.90990991e+00, -9.30930931e+00, -8.70870871e+00,
-8.10810811e+00, -7.50750751e+00, -6.90690691e+00,
-6.30630631e+00, -5.70570571e+00, -5.10510511e+00,
-4.50450450e+00, -3.90390390e+00, -3.30330330e+00,
-2.70270270e+00, -2.10210210e+00, -1.50150150e+00,
-9.00900901e-01, -3.00300300e-01, 3.00300300e-01,
9.00900901e-01, 1.50150150e+00, 2.10210210e+00,
2.70270270e+00, 3.30330330e+00, 3.90390390e+00,
4.50450450e+00, 5.10510511e+00, 5.70570571e+00,
6.30630631e+00, 6.90690691e+00, 7.50750751e+00,
8.10810811e+00, 8.70870871e+00, 9.30930931e+00,
9.90990991e+00, 1.05105105e+01, 1.11111111e+01,
1.17117117e+01, 1.23123123e+01, 1.29129129e+01,
1.35135135e+01, 1.41141141e+01, 1.47147147e+01,
1.53153153e+01, 1.59159159e+01, 1.65165165e+01,
1.71171171e+01, 1.77177177e+01, 1.83183183e+01,
1.89189189e+01, 1.95195195e+01, 2.01201201e+01,
2.07207207e+01, 2.13213213e+01, 2.19219219e+01,
2.25225225e+01, 2.31231231e+01, 2.37237237e+01,
2.43243243e+01, 2.49249249e+01, 2.55255255e+01,
2.61261261e+01, 2.67267267e+01, 2.73273273e+01,
2.79279279e+01, 2.85285285e+01, 2.91291291e+01,
2.97297297e+01, 3.03303303e+01, 3.09309309e+01,
3.15315315e+01, 3.21321321e+01, 3.27327327e+01,
3.33333333e+01, 3.39339339e+01, 3.45345345e+01,
3.51351351e+01, 3.57357357e+01, 3.63363363e+01,
3.69369369e+01, 3.75375375e+01, 3.81381381e+01,
3.87387387e+01, 3.93393393e+01, 3.99399399e+01,
4.05405405e+01, 4.11411411e+01, 4.17417417e+01,
4.23423423e+01, 4.29429429e+01, 4.35435435e+01,
4.41441441e+01, 4.47447447e+01, 4.53453453e+01,
4.59459459e+01, 4.65465465e+01, 4.71471471e+01,
4.77477477e+01, 4.83483483e+01, 4.89489489e+01,
4.95495495e+01, 5.01501502e+01, 5.07507508e+01,
5.13513514e+01, 5.19519520e+01, 5.25525526e+01,
5.31531532e+01, 5.37537538e+01, 5.43543544e+01,
5.49549550e+01, 5.55555556e+01, 5.61561562e+01,
5.67567568e+01, 5.73573574e+01, 5.79579580e+01,
5.85585586e+01, 5.91591592e+01, 5.97597598e+01,
6.03603604e+01, 6.09609610e+01, 6.15615616e+01,
6.21621622e+01, 6.27627628e+01, 6.33633634e+01,
6.39639640e+01, 6.45645646e+01, 6.51651652e+01,
6.57657658e+01, 6.63663664e+01, 6.69669670e+01,
6.75675676e+01, 6.81681682e+01, 6.87687688e+01,
6.93693694e+01, 6.99699700e+01, 7.05705706e+01,
7.11711712e+01, 7.17717718e+01, 7.23723724e+01,
7.29729730e+01, 7.35735736e+01, 7.41741742e+01,
7.47747748e+01, 7.53753754e+01, 7.59759760e+01,
7.65765766e+01, 7.71771772e+01, 7.77777778e+01,
7.83783784e+01, 7.89789790e+01, 7.95795796e+01,
8.01801802e+01, 8.07807808e+01, 8.13813814e+01,
8.19819820e+01, 8.25825826e+01, 8.31831832e+01,
8.37837838e+01, 8.43843844e+01, 8.49849850e+01,
8.55855856e+01, 8.61861862e+01, 8.67867868e+01,
8.73873874e+01, 8.79879880e+01, 8.85885886e+01,
8.91891892e+01, 8.97897898e+01, 9.03903904e+01,
9.09909910e+01, 9.15915916e+01, 9.21921922e+01,
9.27927928e+01, 9.33933934e+01, 9.39939940e+01,
9.45945946e+01, 9.51951952e+01, 9.57957958e+01,
9.63963964e+01, 9.69969970e+01, 9.75975976e+01,
9.81981982e+01, 9.87987988e+01, 9.93993994e+01,
1.00000000e+02, 1.00600601e+02, 1.01201201e+02,
1.01801802e+02, 1.02402402e+02, 1.03003003e+02,
1.03603604e+02, 1.04204204e+02, 1.04804805e+02,
1.05405405e+02, 1.06006006e+02, 1.06606607e+02,
1.07207207e+02, 1.07807808e+02, 1.08408408e+02,
1.09009009e+02, 1.09609610e+02, 1.10210210e+02,
1.10810811e+02, 1.11411411e+02, 1.12012012e+02,
1.12612613e+02, 1.13213213e+02, 1.13813814e+02,
1.14414414e+02, 1.15015015e+02, 1.15615616e+02,
1.16216216e+02, 1.16816817e+02, 1.17417417e+02,
1.18018018e+02, 1.18618619e+02, 1.19219219e+02,
1.19819820e+02, 1.20420420e+02, 1.21021021e+02,
1.21621622e+02, 1.22222222e+02, 1.22822823e+02,
1.23423423e+02, 1.24024024e+02, 1.24624625e+02,
1.25225225e+02, 1.25825826e+02, 1.26426426e+02,
1.27027027e+02, 1.27627628e+02, 1.28228228e+02,
1.28828829e+02, 1.29429429e+02, 1.30030030e+02,
1.30630631e+02, 1.31231231e+02, 1.31831832e+02,
1.32432432e+02, 1.33033033e+02, 1.33633634e+02,
1.34234234e+02, 1.34834835e+02, 1.35435435e+02,
1.36036036e+02, 1.36636637e+02, 1.37237237e+02,
1.37837838e+02, 1.38438438e+02, 1.39039039e+02,
1.39639640e+02, 1.40240240e+02, 1.40840841e+02,
1.41441441e+02, 1.42042042e+02, 1.42642643e+02,
1.43243243e+02, 1.43843844e+02, 1.44444444e+02,
1.45045045e+02, 1.45645646e+02, 1.46246246e+02,
1.46846847e+02, 1.47447447e+02, 1.48048048e+02,
1.48648649e+02, 1.49249249e+02, 1.49849850e+02,
1.50450450e+02, 1.51051051e+02, 1.51651652e+02,
1.52252252e+02, 1.52852853e+02, 1.53453453e+02,
1.54054054e+02, 1.54654655e+02, 1.55255255e+02,
1.55855856e+02, 1.56456456e+02, 1.57057057e+02,
1.57657658e+02, 1.58258258e+02, 1.58858859e+02,
1.59459459e+02, 1.60060060e+02, 1.60660661e+02,
1.61261261e+02, 1.61861862e+02, 1.62462462e+02,
1.63063063e+02, 1.63663664e+02, 1.64264264e+02,
1.64864865e+02, 1.65465465e+02, 1.66066066e+02,
1.66666667e+02, 1.67267267e+02, 1.67867868e+02,
1.68468468e+02, 1.69069069e+02, 1.69669670e+02,
1.70270270e+02, 1.70870871e+02, 1.71471471e+02,
1.72072072e+02, 1.72672673e+02, 1.73273273e+02,
1.73873874e+02, 1.74474474e+02, 1.75075075e+02,
1.75675676e+02, 1.76276276e+02, 1.76876877e+02,
1.77477477e+02, 1.78078078e+02, 1.78678679e+02,
1.79279279e+02, 1.79879880e+02, 1.80480480e+02,
1.81081081e+02, 1.81681682e+02, 1.82282282e+02,
1.82882883e+02, 1.83483483e+02, 1.84084084e+02,
1.84684685e+02, 1.85285285e+02, 1.85885886e+02,
1.86486486e+02, 1.87087087e+02, 1.87687688e+02,
1.88288288e+02, 1.88888889e+02, 1.89489489e+02,
1.90090090e+02, 1.90690691e+02, 1.91291291e+02,
1.91891892e+02, 1.92492492e+02, 1.93093093e+02,
1.93693694e+02, 1.94294294e+02, 1.94894895e+02,
1.95495495e+02, 1.96096096e+02, 1.96696697e+02,
1.97297297e+02, 1.97897898e+02, 1.98498498e+02,
1.99099099e+02, 1.99699700e+02, 2.00300300e+02,
2.00900901e+02, 2.01501502e+02, 2.02102102e+02,
2.02702703e+02, 2.03303303e+02, 2.03903904e+02,
2.04504505e+02, 2.05105105e+02, 2.05705706e+02,
2.06306306e+02, 2.06906907e+02, 2.07507508e+02,
2.08108108e+02, 2.08708709e+02, 2.09309309e+02,
2.09909910e+02, 2.10510511e+02, 2.11111111e+02,
2.11711712e+02, 2.12312312e+02, 2.12912913e+02,
2.13513514e+02, 2.14114114e+02, 2.14714715e+02,
2.15315315e+02, 2.15915916e+02, 2.16516517e+02,
2.17117117e+02, 2.17717718e+02, 2.18318318e+02,
2.18918919e+02, 2.19519520e+02, 2.20120120e+02,
2.20720721e+02, 2.21321321e+02, 2.21921922e+02,
2.22522523e+02, 2.23123123e+02, 2.23723724e+02,
2.24324324e+02, 2.24924925e+02, 2.25525526e+02,
2.26126126e+02, 2.26726727e+02, 2.27327327e+02,
2.27927928e+02, 2.28528529e+02, 2.29129129e+02,
2.29729730e+02, 2.30330330e+02, 2.30930931e+02,
2.31531532e+02, 2.32132132e+02, 2.32732733e+02,
2.33333333e+02, 2.33933934e+02, 2.34534535e+02,
2.35135135e+02, 2.35735736e+02, 2.36336336e+02,
2.36936937e+02, 2.37537538e+02, 2.38138138e+02,
2.38738739e+02, 2.39339339e+02, 2.39939940e+02,
2.40540541e+02, 2.41141141e+02, 2.41741742e+02,
2.42342342e+02, 2.42942943e+02, 2.43543544e+02,
2.44144144e+02, 2.44744745e+02, 2.45345345e+02,
2.45945946e+02, 2.46546547e+02, 2.47147147e+02,
2.47747748e+02, 2.48348348e+02, 2.48948949e+02,
2.49549550e+02, 2.50150150e+02, 2.50750751e+02,
2.51351351e+02, 2.51951952e+02, 2.52552553e+02,
2.53153153e+02, 2.53753754e+02, 2.54354354e+02,
2.54954955e+02, 2.55555556e+02, 2.56156156e+02,
2.56756757e+02, 2.57357357e+02, 2.57957958e+02,
2.58558559e+02, 2.59159159e+02, 2.59759760e+02,
2.60360360e+02, 2.60960961e+02, 2.61561562e+02,
2.62162162e+02, 2.62762763e+02, 2.63363363e+02,
2.63963964e+02, 2.64564565e+02, 2.65165165e+02,
2.65765766e+02, 2.66366366e+02, 2.66966967e+02,
2.67567568e+02, 2.68168168e+02, 2.68768769e+02,
2.69369369e+02, 2.69969970e+02, 2.70570571e+02,
2.71171171e+02, 2.71771772e+02, 2.72372372e+02,
2.72972973e+02, 2.73573574e+02, 2.74174174e+02,
2.74774775e+02, 2.75375375e+02, 2.75975976e+02,
2.76576577e+02, 2.77177177e+02, 2.77777778e+02,
2.78378378e+02, 2.78978979e+02, 2.79579580e+02,
2.80180180e+02, 2.80780781e+02, 2.81381381e+02,
2.81981982e+02, 2.82582583e+02, 2.83183183e+02,
2.83783784e+02, 2.84384384e+02, 2.84984985e+02,
2.85585586e+02, 2.86186186e+02, 2.86786787e+02,
2.87387387e+02, 2.87987988e+02, 2.88588589e+02,
2.89189189e+02, 2.89789790e+02, 2.90390390e+02,
2.90990991e+02, 2.91591592e+02, 2.92192192e+02,
2.92792793e+02, 2.93393393e+02, 2.93993994e+02,
2.94594595e+02, 2.95195195e+02, 2.95795796e+02,
2.96396396e+02, 2.96996997e+02, 2.97597598e+02,
2.98198198e+02, 2.98798799e+02, 2.99399399e+02,
3.00000000e+02, 3.00600601e+02, 3.01201201e+02,
3.01801802e+02, 3.02402402e+02, 3.03003003e+02,
3.03603604e+02, 3.04204204e+02, 3.04804805e+02,
3.05405405e+02, 3.06006006e+02, 3.06606607e+02,
3.07207207e+02, 3.07807808e+02, 3.08408408e+02,
3.09009009e+02, 3.09609610e+02, 3.10210210e+02,
3.10810811e+02, 3.11411411e+02, 3.12012012e+02,
3.12612613e+02, 3.13213213e+02, 3.13813814e+02,
3.14414414e+02, 3.15015015e+02, 3.15615616e+02,
3.16216216e+02, 3.16816817e+02, 3.17417417e+02,
3.18018018e+02, 3.18618619e+02, 3.19219219e+02,
3.19819820e+02, 3.20420420e+02, 3.21021021e+02,
3.21621622e+02, 3.22222222e+02, 3.22822823e+02,
3.23423423e+02, 3.24024024e+02, 3.24624625e+02,
3.25225225e+02, 3.25825826e+02, 3.26426426e+02,
3.27027027e+02, 3.27627628e+02, 3.28228228e+02,
3.28828829e+02, 3.29429429e+02, 3.30030030e+02,
3.30630631e+02, 3.31231231e+02, 3.31831832e+02,
3.32432432e+02, 3.33033033e+02, 3.33633634e+02,
3.34234234e+02, 3.34834835e+02, 3.35435435e+02,
3.36036036e+02, 3.36636637e+02, 3.37237237e+02,
3.37837838e+02, 3.38438438e+02, 3.39039039e+02,
3.39639640e+02, 3.40240240e+02, 3.40840841e+02,
3.41441441e+02, 3.42042042e+02, 3.42642643e+02,
3.43243243e+02, 3.43843844e+02, 3.44444444e+02,
3.45045045e+02, 3.45645646e+02, 3.46246246e+02,
3.46846847e+02, 3.47447447e+02, 3.48048048e+02,
3.48648649e+02, 3.49249249e+02, 3.49849850e+02,
3.50450450e+02, 3.51051051e+02, 3.51651652e+02,
3.52252252e+02, 3.52852853e+02, 3.53453453e+02,
3.54054054e+02, 3.54654655e+02, 3.55255255e+02,
3.55855856e+02, 3.56456456e+02, 3.57057057e+02,
3.57657658e+02, 3.58258258e+02, 3.58858859e+02,
3.59459459e+02, 3.60060060e+02, 3.60660661e+02,
3.61261261e+02, 3.61861862e+02, 3.62462462e+02,
3.63063063e+02, 3.63663664e+02, 3.64264264e+02,
3.64864865e+02, 3.65465465e+02, 3.66066066e+02,
3.66666667e+02, 3.67267267e+02, 3.67867868e+02,
3.68468468e+02, 3.69069069e+02, 3.69669670e+02,
3.70270270e+02, 3.70870871e+02, 3.71471471e+02,
3.72072072e+02, 3.72672673e+02, 3.73273273e+02,
3.73873874e+02, 3.74474474e+02, 3.75075075e+02,
3.75675676e+02, 3.76276276e+02, 3.76876877e+02,
3.77477477e+02, 3.78078078e+02, 3.78678679e+02,
3.79279279e+02, 3.79879880e+02, 3.80480480e+02,
3.81081081e+02, 3.81681682e+02, 3.82282282e+02,
3.82882883e+02, 3.83483483e+02, 3.84084084e+02,
3.84684685e+02, 3.85285285e+02, 3.85885886e+02,
3.86486486e+02, 3.87087087e+02, 3.87687688e+02,
3.88288288e+02, 3.88888889e+02, 3.89489489e+02,
3.90090090e+02, 3.90690691e+02, 3.91291291e+02,
3.91891892e+02, 3.92492492e+02, 3.93093093e+02,
3.93693694e+02, 3.94294294e+02, 3.94894895e+02,
3.95495495e+02, 3.96096096e+02, 3.96696697e+02,
3.97297297e+02, 3.97897898e+02, 3.98498498e+02,
3.99099099e+02, 3.99699700e+02, 4.00300300e+02,
4.00900901e+02, 4.01501502e+02, 4.02102102e+02,
4.02702703e+02, 4.03303303e+02, 4.03903904e+02,
4.04504505e+02, 4.05105105e+02, 4.05705706e+02,
4.06306306e+02, 4.06906907e+02, 4.07507508e+02,
4.08108108e+02, 4.08708709e+02, 4.09309309e+02,
4.09909910e+02, 4.10510511e+02, 4.11111111e+02,
4.11711712e+02, 4.12312312e+02, 4.12912913e+02,
4.13513514e+02, 4.14114114e+02, 4.14714715e+02,
4.15315315e+02, 4.15915916e+02, 4.16516517e+02,
4.17117117e+02, 4.17717718e+02, 4.18318318e+02,
4.18918919e+02, 4.19519520e+02, 4.20120120e+02,
4.20720721e+02, 4.21321321e+02, 4.21921922e+02,
4.22522523e+02, 4.23123123e+02, 4.23723724e+02,
4.24324324e+02, 4.24924925e+02, 4.25525526e+02,
4.26126126e+02, 4.26726727e+02, 4.27327327e+02,
4.27927928e+02, 4.28528529e+02, 4.29129129e+02,
4.29729730e+02, 4.30330330e+02, 4.30930931e+02,
4.31531532e+02, 4.32132132e+02, 4.32732733e+02,
4.33333333e+02, 4.33933934e+02, 4.34534535e+02,
4.35135135e+02, 4.35735736e+02, 4.36336336e+02,
4.36936937e+02, 4.37537538e+02, 4.38138138e+02,
4.38738739e+02, 4.39339339e+02, 4.39939940e+02,
4.40540541e+02, 4.41141141e+02, 4.41741742e+02,
4.42342342e+02, 4.42942943e+02, 4.43543544e+02,
4.44144144e+02, 4.44744745e+02, 4.45345345e+02,
4.45945946e+02, 4.46546547e+02, 4.47147147e+02,
4.47747748e+02, 4.48348348e+02, 4.48948949e+02,
4.49549550e+02, 4.50150150e+02, 4.50750751e+02,
4.51351351e+02, 4.51951952e+02, 4.52552553e+02,
4.53153153e+02, 4.53753754e+02, 4.54354354e+02,
4.54954955e+02, 4.55555556e+02, 4.56156156e+02,
4.56756757e+02, 4.57357357e+02, 4.57957958e+02,
4.58558559e+02, 4.59159159e+02, 4.59759760e+02,
4.60360360e+02, 4.60960961e+02, 4.61561562e+02,
4.62162162e+02, 4.62762763e+02, 4.63363363e+02,
4.63963964e+02, 4.64564565e+02, 4.65165165e+02,
4.65765766e+02, 4.66366366e+02, 4.66966967e+02,
4.67567568e+02, 4.68168168e+02, 4.68768769e+02,
4.69369369e+02, 4.69969970e+02, 4.70570571e+02,
4.71171171e+02, 4.71771772e+02, 4.72372372e+02,
4.72972973e+02, 4.73573574e+02, 4.74174174e+02,
4.74774775e+02, 4.75375375e+02, 4.75975976e+02,
4.76576577e+02, 4.77177177e+02, 4.77777778e+02,
4.78378378e+02, 4.78978979e+02, 4.79579580e+02,
4.80180180e+02, 4.80780781e+02, 4.81381381e+02,
4.81981982e+02, 4.82582583e+02, 4.83183183e+02,
4.83783784e+02, 4.84384384e+02, 4.84984985e+02,
4.85585586e+02, 4.86186186e+02, 4.86786787e+02,
4.87387387e+02, 4.87987988e+02, 4.88588589e+02,
4.89189189e+02, 4.89789790e+02, 4.90390390e+02,
4.90990991e+02, 4.91591592e+02, 4.92192192e+02,
4.92792793e+02, 4.93393393e+02, 4.93993994e+02,
4.94594595e+02, 4.95195195e+02, 4.95795796e+02,
4.96396396e+02, 4.96996997e+02, 4.97597598e+02,
4.98198198e+02, 4.98798799e+02, 4.99399399e+02,
5.00000000e+02])
In [84]:
F = t / 360
In [85]:
F
Out[85]:
array([ -2.77777778e-01, -2.76109443e-01, -2.74441108e-01,
-2.72772773e-01, -2.71104438e-01, -2.69436103e-01,
-2.67767768e-01, -2.66099433e-01, -2.64431098e-01,
-2.62762763e-01, -2.61094428e-01, -2.59426093e-01,
-2.57757758e-01, -2.56089423e-01, -2.54421088e-01,
-2.52752753e-01, -2.51084418e-01, -2.49416083e-01,
-2.47747748e-01, -2.46079413e-01, -2.44411078e-01,
-2.42742743e-01, -2.41074408e-01, -2.39406073e-01,
-2.37737738e-01, -2.36069403e-01, -2.34401068e-01,
-2.32732733e-01, -2.31064398e-01, -2.29396063e-01,
-2.27727728e-01, -2.26059393e-01, -2.24391058e-01,
-2.22722723e-01, -2.21054388e-01, -2.19386053e-01,
-2.17717718e-01, -2.16049383e-01, -2.14381048e-01,
-2.12712713e-01, -2.11044378e-01, -2.09376043e-01,
-2.07707708e-01, -2.06039373e-01, -2.04371038e-01,
-2.02702703e-01, -2.01034368e-01, -1.99366033e-01,
-1.97697698e-01, -1.96029363e-01, -1.94361028e-01,
-1.92692693e-01, -1.91024358e-01, -1.89356023e-01,
-1.87687688e-01, -1.86019353e-01, -1.84351018e-01,
-1.82682683e-01, -1.81014348e-01, -1.79346013e-01,
-1.77677678e-01, -1.76009343e-01, -1.74341008e-01,
-1.72672673e-01, -1.71004338e-01, -1.69336003e-01,
-1.67667668e-01, -1.65999333e-01, -1.64330998e-01,
-1.62662663e-01, -1.60994328e-01, -1.59325993e-01,
-1.57657658e-01, -1.55989323e-01, -1.54320988e-01,
-1.52652653e-01, -1.50984318e-01, -1.49315983e-01,
-1.47647648e-01, -1.45979313e-01, -1.44310978e-01,
-1.42642643e-01, -1.40974308e-01, -1.39305973e-01,
-1.37637638e-01, -1.35969303e-01, -1.34300968e-01,
-1.32632633e-01, -1.30964298e-01, -1.29295963e-01,
-1.27627628e-01, -1.25959293e-01, -1.24290958e-01,
-1.22622623e-01, -1.20954288e-01, -1.19285953e-01,
-1.17617618e-01, -1.15949283e-01, -1.14280948e-01,
-1.12612613e-01, -1.10944278e-01, -1.09275943e-01,
-1.07607608e-01, -1.05939273e-01, -1.04270938e-01,
-1.02602603e-01, -1.00934268e-01, -9.92659326e-02,
-9.75975976e-02, -9.59292626e-02, -9.42609276e-02,
-9.25925926e-02, -9.09242576e-02, -8.92559226e-02,
-8.75875876e-02, -8.59192526e-02, -8.42509176e-02,
-8.25825826e-02, -8.09142476e-02, -7.92459126e-02,
-7.75775776e-02, -7.59092426e-02, -7.42409076e-02,
-7.25725726e-02, -7.09042376e-02, -6.92359026e-02,
-6.75675676e-02, -6.58992326e-02, -6.42308976e-02,
-6.25625626e-02, -6.08942276e-02, -5.92258926e-02,
-5.75575576e-02, -5.58892226e-02, -5.42208876e-02,
-5.25525526e-02, -5.08842176e-02, -4.92158825e-02,
-4.75475475e-02, -4.58792125e-02, -4.42108775e-02,
-4.25425425e-02, -4.08742075e-02, -3.92058725e-02,
-3.75375375e-02, -3.58692025e-02, -3.42008675e-02,
-3.25325325e-02, -3.08641975e-02, -2.91958625e-02,
-2.75275275e-02, -2.58591925e-02, -2.41908575e-02,
-2.25225225e-02, -2.08541875e-02, -1.91858525e-02,
-1.75175175e-02, -1.58491825e-02, -1.41808475e-02,
-1.25125125e-02, -1.08441775e-02, -9.17584251e-03,
-7.50750751e-03, -5.83917251e-03, -4.17083750e-03,
-2.50250250e-03, -8.34167501e-04, 8.34167501e-04,
2.50250250e-03, 4.17083750e-03, 5.83917251e-03,
7.50750751e-03, 9.17584251e-03, 1.08441775e-02,
1.25125125e-02, 1.41808475e-02, 1.58491825e-02,
1.75175175e-02, 1.91858525e-02, 2.08541875e-02,
2.25225225e-02, 2.41908575e-02, 2.58591925e-02,
2.75275275e-02, 2.91958625e-02, 3.08641975e-02,
3.25325325e-02, 3.42008675e-02, 3.58692025e-02,
3.75375375e-02, 3.92058725e-02, 4.08742075e-02,
4.25425425e-02, 4.42108775e-02, 4.58792125e-02,
4.75475475e-02, 4.92158825e-02, 5.08842176e-02,
5.25525526e-02, 5.42208876e-02, 5.58892226e-02,
5.75575576e-02, 5.92258926e-02, 6.08942276e-02,
6.25625626e-02, 6.42308976e-02, 6.58992326e-02,
6.75675676e-02, 6.92359026e-02, 7.09042376e-02,
7.25725726e-02, 7.42409076e-02, 7.59092426e-02,
7.75775776e-02, 7.92459126e-02, 8.09142476e-02,
8.25825826e-02, 8.42509176e-02, 8.59192526e-02,
8.75875876e-02, 8.92559226e-02, 9.09242576e-02,
9.25925926e-02, 9.42609276e-02, 9.59292626e-02,
9.75975976e-02, 9.92659326e-02, 1.00934268e-01,
1.02602603e-01, 1.04270938e-01, 1.05939273e-01,
1.07607608e-01, 1.09275943e-01, 1.10944278e-01,
1.12612613e-01, 1.14280948e-01, 1.15949283e-01,
1.17617618e-01, 1.19285953e-01, 1.20954288e-01,
1.22622623e-01, 1.24290958e-01, 1.25959293e-01,
1.27627628e-01, 1.29295963e-01, 1.30964298e-01,
1.32632633e-01, 1.34300968e-01, 1.35969303e-01,
1.37637638e-01, 1.39305973e-01, 1.40974308e-01,
1.42642643e-01, 1.44310978e-01, 1.45979313e-01,
1.47647648e-01, 1.49315983e-01, 1.50984318e-01,
1.52652653e-01, 1.54320988e-01, 1.55989323e-01,
1.57657658e-01, 1.59325993e-01, 1.60994328e-01,
1.62662663e-01, 1.64330998e-01, 1.65999333e-01,
1.67667668e-01, 1.69336003e-01, 1.71004338e-01,
1.72672673e-01, 1.74341008e-01, 1.76009343e-01,
1.77677678e-01, 1.79346013e-01, 1.81014348e-01,
1.82682683e-01, 1.84351018e-01, 1.86019353e-01,
1.87687688e-01, 1.89356023e-01, 1.91024358e-01,
1.92692693e-01, 1.94361028e-01, 1.96029363e-01,
1.97697698e-01, 1.99366033e-01, 2.01034368e-01,
2.02702703e-01, 2.04371038e-01, 2.06039373e-01,
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1.38388388e+00, 1.38555222e+00, 1.38722055e+00,
1.38888889e+00])
In [86]:
F[t < 0] = 0
F[t > 360] = 1
F
Out[86]:
array([ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
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1.00000000e+00, 1.00000000e+00, 1.00000000e+00,
1.00000000e+00, 1.00000000e+00, 1.00000000e+00,
1.00000000e+00, 1.00000000e+00, 1.00000000e+00,
1.00000000e+00])
In [87]:
f = np.gradient(F)
In [90]:
plt.plot(t,f)
plt.ylim(-0.0001, f.max()*1.1)
plt.xticks([0, 180, 360]);
plt.title("Probability Density Function")
plt.xlabel("$x$ (deg.)");
plt.ylabel("$f(x)$");
In [ ]:
Content source: rrbb014/fastcampus_dss
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