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# Module: tfp.distributions

Statistical distributions.

Defined in `python/distributions/__init__.py`.

## Classes

`class Cauchy`: The Cauchy distribution with location `loc` and scale `scale`.

`class ConditionalDistribution`: Distribution that supports intrinsic parameters (local latents).

`class ConditionalTransformedDistribution`: A TransformedDistribution that allows intrinsic conditioning.

`class ReparameterizationType`: Instances of this class represent how sampling is reparameterized.

`class Distribution`: A generic probability distribution base class.

`class Autoregressive`: Autoregressive distributions.

`class BatchReshape`: The Batch-Reshaping distribution.

`class Bernoulli`: Bernoulli distribution.

`class Beta`: Beta distribution.

`class Binomial`: Binomial distribution.

`class Blockwise`: Blockwise distribution.

`class Categorical`: Categorical distribution over integers.

`class Chi`: Chi distribution.

`class Chi2`: Chi2 distribution.

`class Chi2WithAbsDf`: Chi2 with parameter transform `df = floor(abs(df))`.

`class Deterministic`: Scalar `Deterministic` distribution on the real line.

`class VectorDeterministic`: Vector `Deterministic` distribution on `R^k`.

`class Empirical`: Empirical distribution.

`class Exponential`: Exponential distribution.

`class VectorExponentialDiag`: The vectorization of the Exponential distribution on `R^k`.

`class Gamma`: Gamma distribution.

`class GammaGamma`: Gamma-Gamma distribution.

`class InverseGaussian`: Inverse Gaussian distribution.

`class Geometric`: Geometric distribution.

`class GaussianProcess`: Marginal distribution of a Gaussian process at finitely many points.

`class GaussianProcessRegressionModel`: Posterior predictive distribution in a conjugate GP regression model.

`class VariationalGaussianProcess`: Posterior predictive of a variational Gaussian process.

`class Gumbel`: The scalar Gumbel distribution with location `loc` and `scale` parameters.

`class HalfCauchy`: Half-Cauchy distribution.

`class HalfNormal`: The Half Normal distribution with scale `scale`.

`class HiddenMarkovModel`: Hidden Markov model distribution.

`class Horseshoe`: Horseshoe distribution.

`class Independent`: Independent distribution from batch of distributions.

`class InverseGamma`: InverseGamma distribution.

`class JointDistribution`: Joint distribution over one or more component distributions.

`class JointDistributionCoroutine`: Joint distribution parameterized by a distribution-making generator.

`class JointDistributionNamed`: Joint distribution parameterized by named distribution-making functions.

`class JointDistributionSequential`: Joint distribution parameterized by distribution-making functions.

`class Kumaraswamy`: Kumaraswamy distribution.

`class LinearGaussianStateSpaceModel`: Observation distribution from a linear Gaussian state space model.

`class Laplace`: The Laplace distribution with location `loc` and `scale` parameters.

`class LKJ`: The LKJ distribution on correlation matrices.

`class Logistic`: The Logistic distribution with location `loc` and `scale` parameters.

`class LogNormal`: The log-normal distribution.

`class NegativeBinomial`: NegativeBinomial distribution.

`class Normal`: The Normal distribution with location `loc` and `scale` parameters.

`class Poisson`: Poisson distribution.

`class PoissonLogNormalQuadratureCompound`: `PoissonLogNormalQuadratureCompound` distribution.

`class Sample`: Sample distribution via independent draws.

`class SeedStream`: Local PRNG for amplifying seed entropy into seeds for base operations.

`class SinhArcsinh`: The SinhArcsinh transformation of a distribution on `(-inf, inf)`.

`class StudentT`: Student's t-distribution.

`class StudentTProcess`: Marginal distribution of a Student's T process at finitely many points.

`class Triangular`: Triangular distribution with `low`, `high` and `peak` parameters.

`class TruncatedNormal`: The Truncated Normal distribution.

`class Uniform`: Uniform distribution with `low` and `high` parameters.

`class MultivariateNormalDiag`: The multivariate normal distribution on `R^k`.

`class MultivariateNormalFullCovariance`: The multivariate normal distribution on `R^k`.

`class MultivariateNormalLinearOperator`: The multivariate normal distribution on `R^k`.

`class MultivariateNormalTriL`: The multivariate normal distribution on `R^k`.

`class MultivariateNormalDiagPlusLowRank`: The multivariate normal distribution on `R^k`.

`class MultivariateNormalDiagWithSoftplusScale`: MultivariateNormalDiag with `diag_stddev = softplus(diag_stddev)`.

`class MultivariateStudentTLinearOperator`: The [Multivariate Student's t-distribution](

`class Dirichlet`: Dirichlet distribution.

`class DirichletMultinomial`: Dirichlet-Multinomial compound distribution.

`class Multinomial`: Multinomial distribution.

`class VectorDiffeomixture`: VectorDiffeomixture distribution.

`class VectorLaplaceDiag`: The vectorization of the Laplace distribution on `R^k`.

`class VectorSinhArcsinhDiag`: The (diagonal) SinhArcsinh transformation of a distribution on `R^k`.

`class VonMises`: The von Mises distribution over angles.

`class VonMisesFisher`: The von Mises-Fisher distribution over unit vectors on `S^{n-1}`.

`class Wishart`: The matrix Wishart distribution on positive definite matrices.

`class TransformedDistribution`: A Transformed Distribution.

`class QuantizedDistribution`: Distribution representing the quantization `Y = ceiling(X)`.

`class Mixture`: Mixture distribution.

`class MixtureSameFamily`: Mixture (same-family) distribution.

`class ExpRelaxedOneHotCategorical`: ExpRelaxedOneHotCategorical distribution with temperature and logits.

`class OneHotCategorical`: OneHotCategorical distribution.

`class Pareto`: Pareto distribution.

`class RelaxedBernoulli`: RelaxedBernoulli distribution with temperature and logits parameters.

`class RelaxedOneHotCategorical`: RelaxedOneHotCategorical distribution with temperature and logits.

`class Zipf`: Zipf distribution.

`class RegisterKL`: Decorator to register a KL divergence implementation function.

## Functions

`InverseGammaWithSoftplusConcentrationRate(...)`: `InverseGamma` with softplus of `concentration` and `scale`. (deprecated)

`InverseGammaWithSoftplusConcentrationScale(...)`: `InverseGamma` with softplus of `concentration` and `scale`. (deprecated)

`kl_divergence(...)`: Get the KL-divergence KL(distribution_a || distribution_b).

`fill_triangular(...)`: Creates a (batch of) triangular matrix from a vector of inputs.

`fill_triangular_inverse(...)`: Creates a vector from a (batch of) triangular matrix.

`matrix_diag_transform(...)`: Transform diagonal of [batch-]matrix, leave rest of matrix unchanged.

`reduce_weighted_logsumexp(...)`: Computes `log(abs(sum(weight * exp(elements across tensor dimensions))))`.

`softplus_inverse(...)`: Computes the inverse softplus, i.e., x = softplus_inverse(softplus(x)).

`tridiag(...)`: Creates a matrix with values set above, below, and on the diagonal.

`normal_conjugates_known_scale_posterior(...)`: Posterior Normal distribution with conjugate prior on the mean.

`normal_conjugates_known_scale_predictive(...)`: Posterior predictive Normal distribution w. conjugate prior on the mean.

`assign_moving_mean_variance(...)`: Compute exponentially weighted moving {mean,variance} of a streaming value.

`assign_log_moving_mean_exp(...)`: Compute the log of the exponentially weighted moving mean of the exp.

`moving_mean_variance(...)`: Compute exponentially weighted moving {mean,variance} of a streaming value. (deprecated)

`quadrature_scheme_softmaxnormal_gauss_hermite(...)`: Use Gauss-Hermite quadrature to form quadrature on `K - 1` simplex.

`quadrature_scheme_softmaxnormal_quantiles(...)`: Use SoftmaxNormal quantiles to form quadrature on `K - 1` simplex.

`quadrature_scheme_lognormal_gauss_hermite(...)`: Use Gauss-Hermite quadrature to form quadrature on positive-reals.

`quadrature_scheme_lognormal_quantiles(...)`: Use LogNormal quantiles to form quadrature on positive-reals.