class tf.contrib.distributions.Exponential
See the guide: Statistical Distributions (contrib) > Univariate (scalar) distributions
The Exponential distribution with rate parameter lam.
The PDF of this distribution is:
prob(x) = (lam * e^(-lam * x)), x > 0
Note that the Exponential distribution is a special case of the Gamma distribution, with Exponential(lam) = Gamma(1, lam).
allow_nan_stats
Python boolean describing behavior when a stat is undefined.
Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)^2] is also undefined.
allow_nan_stats
: Python boolean.alpha
Shape parameter.
beta
Inverse scale parameter.
dtype
The DType
of Tensor
s handled by this Distribution
.
is_continuous
is_reparameterized
lam
name
Name prepended to all ops created by this Distribution
.
parameters
Dictionary of parameters used to instantiate this Distribution
.
validate_args
Python boolean indicated possibly expensive checks are enabled.
__init__(lam, validate_args=False, allow_nan_stats=True, name='Exponential')
Construct Exponential distribution with parameter lam
.
lam
: Floating point tensor, the rate of the distribution(s). lam
must contain only positive values.validate_args
: Boolean
, default False
. Whether to assert that lam > 0
, and that x > 0
in the methods prob(x)
and log_prob(x)
. If validate_args
is False
and the inputs are invalid, correct behavior is not guaranteed.allow_nan_stats
: Boolean
, default True
. If False
, raise an exception if a statistic (e.g. mean/mode/etc...) is undefined for any batch member. If True
, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.name
: The name to prepend to all ops created by this distribution.batch_shape(name='batch_shape')
Shape of a single sample from a single event index as a 1-D Tensor
.
The product of the dimensions of the batch_shape
is the number of independent distributions of this kind the instance represents.
name
: name to give to the opbatch_shape
: Tensor
.cdf(value, name='cdf', **condition_kwargs)
Cumulative distribution function.
Given random variable X
, the cumulative distribution function cdf
is:
cdf(x) := P[X <= x]
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.cdf
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.copy(**override_parameters_kwargs)
Creates a deep copy of the distribution.
Note: the copy distribution may continue to depend on the original intialization arguments.
**override_parameters_kwargs: String/value dictionary of initialization arguments to override with new values.
distribution
: A new instance of type(self)
intitialized from the union of self.parameters and override_parameters_kwargs, i.e., dict(self.parameters, **override_parameters_kwargs)
.entropy(name='entropy')
Shannon entropy in nats.
Additional documentation from Gamma
:
This is defined to be
entropy = alpha - log(beta) + log(Gamma(alpha)) + (1-alpha)digamma(alpha)
where digamma(alpha) is the digamma function.
event_shape(name='event_shape')
Shape of a single sample from a single batch as a 1-D int32 Tensor
.
name
: name to give to the opevent_shape
: Tensor
.get_batch_shape()
Shape of a single sample from a single event index as a TensorShape
.
Same meaning as batch_shape
. May be only partially defined.
batch_shape
: TensorShape
, possibly unknown.get_event_shape()
Shape of a single sample from a single batch as a TensorShape
.
Same meaning as event_shape
. May be only partially defined.
event_shape
: TensorShape
, possibly unknown.is_scalar_batch(name='is_scalar_batch')
Indicates that batch_shape == []
.
name
: The name to give this op.is_scalar_batch
: Boolean
scalar
Tensor
.is_scalar_event(name='is_scalar_event')
Indicates that event_shape == []
.
name
: The name to give this op.is_scalar_event
: Boolean
scalar
Tensor
.log_cdf(value, name='log_cdf', **condition_kwargs)
Log cumulative distribution function.
Given random variable X
, the cumulative distribution function cdf
is:
log_cdf(x) := Log[ P[X <= x] ]
Often, a numerical approximation can be used for log_cdf(x)
that yields a more accurate answer than simply taking the logarithm of the cdf
when x << -1
.
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.logcdf
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.log_pdf(value, name='log_pdf', **condition_kwargs)
Log probability density function.
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.log_prob
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.TypeError
: if not is_continuous
.log_pmf(value, name='log_pmf', **condition_kwargs)
Log probability mass function.
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.log_pmf
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.TypeError
: if is_continuous
.log_prob(value, name='log_prob', **condition_kwargs)
Log probability density/mass function (depending on is_continuous
).
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.log_prob
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.log_survival_function(value, name='log_survival_function', **condition_kwargs)
Log survival function.
Given random variable X
, the survival function is defined:
log_survival_function(x) = Log[ P[X > x] ] = Log[ 1 - P[X <= x] ] = Log[ 1 - cdf(x) ]
Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x)
when x >> 1
.
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.
mean(name='mean')
Mean.
mode(name='mode')
Mode.
Additional documentation from Gamma
:
The mode of a gamma distribution is (alpha - 1) / beta
when alpha > 1
, and NaN
otherwise. If self.allow_nan_stats
is False
, an exception will be raised rather than returning NaN
.
param_shapes(cls, sample_shape, name='DistributionParamShapes')
Shapes of parameters given the desired shape of a call to sample()
.
Subclasses should override static method _param_shapes
.
sample_shape
: Tensor
or python list/tuple. Desired shape of a call to sample()
.name
: name to prepend ops with.dict
of parameter name to Tensor
shapes.
param_static_shapes(cls, sample_shape)
param_shapes with static (i.e. TensorShape) shapes.
sample_shape
: TensorShape
or python list/tuple. Desired shape of a call to sample()
.dict
of parameter name to TensorShape
.
ValueError
: if sample_shape
is a TensorShape
and is not fully defined.pdf(value, name='pdf', **condition_kwargs)
Probability density function.
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.prob
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.TypeError
: if not is_continuous
.pmf(value, name='pmf', **condition_kwargs)
Probability mass function.
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.pmf
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.TypeError
: if is_continuous
.prob(value, name='prob', **condition_kwargs)
Probability density/mass function (depending on is_continuous
).
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.prob
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.sample(sample_shape=(), seed=None, name='sample', **condition_kwargs)
Generate samples of the specified shape.
Note that a call to sample()
without arguments will generate a single sample.
sample_shape
: 0D or 1D int32
Tensor
. Shape of the generated samples.seed
: Python integer seed for RNGname
: name to give to the op. **condition_kwargs: Named arguments forwarded to subclass implementation.samples
: a Tensor
with prepended dimensions sample_shape
.std(name='std')
Standard deviation.
survival_function(value, name='survival_function', **condition_kwargs)
Survival function.
Given random variable X
, the survival function is defined:
survival_function(x) = P[X > x] = 1 - P[X <= x] = 1 - cdf(x).
value
: float
or double
Tensor
.name
: The name to give this op. **condition_kwargs: Named arguments forwarded to subclass implementation.Tensorof shape
sample_shape(x) + self.batch_shapewith values of type
self.dtype`.
variance(name='variance')
Variance.
Defined in tensorflow/contrib/distributions/python/ops/exponential.py
.
© 2017 The TensorFlow Authors. All rights reserved.
Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/api_docs/python/tf/contrib/distributions/Exponential