Univariate Normal Distribution

breze.arch.component.distributions.normal.pdf(sample, location=0, scale=1)

Return a theano expression representing the values of the probability density function of a Gaussian distribution.

Parameters:

sample : Theano variable

Array of shape (n,) where n is the number of samples.

location : Theano variable

Scalar representing the mean of the distribution.

scale : Theano variable

Scalar representing the standard deviation of the distribution.

Returns:

l : Theano variable

Array of shape (n,) where each entry represents the density of the corresponding sample.

Examples

>>> import theano
>>> import theano.tensor as T
>>> import numpy as np
>>> from breze.learn.utils import theano_floatx
>>> sample, mean, std = T.vector(), T.scalar(), T.scalar()
>>> p = pdf(sample, mean, std)
>>> f_p = theano.function([sample, mean, std], p)

>>> X, = theano_floatx(np.array([-1, 0, 1]))
>>> ps = f_p(X, 0.1, 1.2)
>>> np.allclose(ps,  [0.21840613,  0.33129956,  0.25094786])
True

breze.arch.component.distributions.normal.cdf(sample, location=0, scale=1)

Return a theano expression representing the values of the cumulative density function of a Gaussian distribution.

Parameters:

sample : Theano variable

Array of shape (n,) where n is the number of samples.

location : Theano variable

Scalar representing the mean of the distribution.

scale : Theano variable

Scalar representing the standard deviation of the distribution.

Returns:

l : Theano variable

Array of shape (n,) where each entry represents the cumulative density of the corresponding sample.

Examples

>>> import theano
>>> import theano.tensor as T
>>> import numpy as np
>>> from breze.learn.utils import theano_floatx
>>> sample, mean, std = T.vector(), T.scalar(), T.scalar()
>>> c = cdf(sample, mean, std)
>>> f_c = theano.function([sample, mean, std], c)

>>> X, = theano_floatx(np.array([-1, 0, 1]))
>>> cs = f_c(X, 0.1, 1.2)
>>> np.allclose(cs, [0.17965868, 0.46679324, 0.77337265])
True