The Normal distribution with location loc and scale parameters.

Inherits From: Distribution

Mathematical details

The probability density function (pdf) is,

pdf(x; mu, sigma) = exp(-0.5 (x - mu)**2 / sigma**2) / Z
Z = (2 pi sigma**2)**0.5

where loc = mu is the mean, scale = sigma is the std. deviation, and, Z is the normalization constant.

The Normal distribution is a member of the location-scale family, i.e., it can be constructed as,

X ~ Normal(loc=0, scale=1)
Y = loc + scale * X


Examples of initialization of one or a batch of distributions.

import tensorflow_probability as tfp
tfd = tfp.distributions

# Define a single scalar Normal distribution.
dist = tfd.Normal(loc=0., scale=3.)

# Evaluate the cdf at 1, returning a scalar.

# Define a batch of two scalar valued Normals.
# The first has mean 1 and standard deviation 11, the second 2 and 22.
dist = tfd.Normal(loc=[1, 2.], scale=[11, 22.])

# Evaluate the pdf of the first distribution on 0, and the second on 1.5,
# returning a length two tensor.
dist.prob([0, 1.5])

# Get 3 samples, returning a 3 x 2 tensor.

Arguments are broadcast when possible.

# Define a batch of two scalar valued Normals.
# Both have mean 1, but different standard deviations.
dist = tfd.Normal(loc=1., scale=[11, 22.])

# Evaluate the pdf of both distributions on the same point, 3.0,
# returning a length 2 tensor.

loc Floating point tensor; the means of the distribution(s).
scale Floating point tensor; the stddevs of the distribution(s). Must contain only positive values.
validate_args Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats Python bool, default True. When