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The Normal distribution with location
tf.compat.v1.distributions.Normal( loc, scale, validate_args=False, allow_nan_stats=True, name='Normal' )
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
loc = mu is the mean,
scale = sigma is the std. deviation, and,
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. dist.cdf(1.) # 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. dist.sample()
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. dist.prob(3.0)
||Floating point tensor; the means of the distribution(s).|
||Floating point tensor; the stddevs of the distribution(s). Must contain only positive values.|