import torch
import matplotlib.pyplot as plt
import seaborn as sns
sns.reset_defaults()
#sns.set_context(context="talk", font_scale=1)
%matplotlib inline
%config InlineBackend.figure_format='retina'

import matplotlib as mpl

mpl.rcParams['axes.spines.right'] = False
mpl.rcParams['axes.spines.top'] = False

dist = torch.distributions

normal = dist.Normal(loc = 0., scale = 1.)
normal

Normal(loc: 0.0, scale: 1.0)

Properties of RV

normal.mean

tensor(0.)

normal.loc

tensor(0.)

normal.scale

tensor(1.)

normal.stddev

tensor(1.)

normal.arg_constraints

{'loc': Real(), 'scale': GreaterThan(lower_bound=0.0)}

Drawing samples

sample = normal.sample([1000])

sns.displot(sample)

<seaborn.axisgrid.FacetGrid at 0x15e71b5e0>

sns.displot(sample, kind='kde',bw_adjust=2, rug=True)

<seaborn.axisgrid.FacetGrid at 0x15ea847c0>

Finding pdf at a given point

normal.log_prob(torch.tensor([1.]))

Plotting pdf over given range

x = torch.linspace(-5., 5., 100)

pdf_x = normal.log_prob(x).exp()

plt.plot(x, pdf_x)
plt.xlabel("x")
plt.ylabel("PDF")

Text(0, 0.5, 'PDF')

Finding cdf at a given point

plt.plot(x, normal.cdf(x))

[<matplotlib.lines.Line2D at 0x15ed35670>]

[x for x in dir(normal) if "__" not in x]

['_batch_shape',
 '_event_shape',
 '_extended_shape',
 '_get_checked_instance',
 '_log_normalizer',
 '_mean_carrier_measure',
 '_natural_params',
 '_validate_args',
 '_validate_sample',
 'arg_constraints',
 'batch_shape',
 'cdf',
 'entropy',
 'enumerate_support',
 'event_shape',
 'expand',
 'has_enumerate_support',
 'has_rsample',
 'icdf',
 'loc',
 'log_prob',
 'mean',
 'perplexity',
 'rsample',
 'sample',
 'sample_n',
 'scale',
 'set_default_validate_args',
 'stddev',
 'support',
 'variance']

normal.support

Real()

normal.entropy()

tensor(1.4189)

dist.Normal(1., 1).entropy()

tensor(1.4189)

dist.Normal(1., 2).entropy()

tensor(2.1121)

normal.perplexity()

tensor(4.1327)