The NegativeBinomial distribution is related to the experiment of performing Bernoulli trials in sequence. Given a Bernoulli trial with probability p of success, the NegativeBinomial distribution represents the distribution over the number of successes s that occur until we observe f failures.

tfd_negative_binomial(
total_count,
logits = NULL,
probs = NULL,
validate_args = FALSE,
allow_nan_stats = TRUE,
name = "NegativeBinomial"
)

## Arguments

total_count Non-negative floating-point Tensor with shape broadcastable to [B1,..., Bb] with b >= 0 and the same dtype as probs or logits. Defines this as a batch of N1 x ... x Nm different Negative Binomial distributions. In practice, this represents the number of negative Bernoulli trials to stop at (the total_count of failures), but this is still a valid distribution when total_count is a non-integer. Floating-point Tensor with shape broadcastable to [B1, ..., Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents logits for the probability of success for independent Negative Binomial distributions and must be in the open interval (-inf, inf). Only one of logits or probs should be specified. Positive floating-point Tensor with shape broadcastable to [B1, ..., Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents the probability of success for independent Negative Binomial distributions and must be in the open interval (0, 1). Only one of logits or probs should be specified. Logical, default FALSE. When TRUE distribution parameters are checked for validity despite possibly degrading runtime performance. When FALSE invalid inputs may silently render incorrect outputs. Default value: FALSE. Logical, default TRUE. When TRUE, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When FALSE, an exception is raised if one or more of the statistic's batch members are undefined. name prefixed to Ops created by this class.

## Value

a distribution instance.

## Details

The probability mass function (pmf) is,

pmf(s; f, p) = p**s (1 - p)**f / Z
Z = s! (f - 1)! / (s + f - 1)!


where:

• total_count = f,

• probs = p,

• Z is the normalizaing constant, and,

• n! is the factorial of n.

For usage examples see e.g. tfd_sample(), tfd_log_prob(), tfd_mean().
Other distributions: tfd_autoregressive(), tfd_batch_reshape(), tfd_bates(), tfd_bernoulli(), tfd_beta_binomial(), tfd_beta(), tfd_binomial(), tfd_categorical(), tfd_cauchy(), tfd_chi2(), tfd_chi(), tfd_cholesky_lkj(), tfd_continuous_bernoulli(), tfd_deterministic(), tfd_dirichlet_multinomial(), tfd_dirichlet(), tfd_empirical(), tfd_exp_gamma(), tfd_exp_inverse_gamma(), tfd_exponential(), tfd_gamma_gamma(), tfd_gamma(), tfd_gaussian_process_regression_model(), tfd_gaussian_process(), tfd_generalized_normal(), tfd_geometric(), tfd_gumbel(), tfd_half_cauchy(), tfd_half_normal(), tfd_hidden_markov_model(), tfd_horseshoe(), tfd_independent(), tfd_inverse_gamma(), tfd_inverse_gaussian(), tfd_johnson_s_u(), tfd_joint_distribution_named_auto_batched(), tfd_joint_distribution_named(), tfd_joint_distribution_sequential_auto_batched(), tfd_joint_distribution_sequential(), tfd_kumaraswamy(), tfd_laplace(), tfd_linear_gaussian_state_space_model(), tfd_lkj(), tfd_log_logistic(), tfd_log_normal(), tfd_logistic(), tfd_mixture_same_family(), tfd_mixture(), tfd_multinomial(), tfd_multivariate_normal_diag_plus_low_rank(), tfd_multivariate_normal_diag(), tfd_multivariate_normal_full_covariance(), tfd_multivariate_normal_linear_operator(), tfd_multivariate_normal_tri_l(), tfd_multivariate_student_t_linear_operator(), tfd_normal(), tfd_one_hot_categorical(), tfd_pareto(), tfd_pixel_cnn(), tfd_poisson_log_normal_quadrature_compound(), tfd_poisson(), tfd_power_spherical(), tfd_probit_bernoulli(), tfd_quantized(), tfd_relaxed_bernoulli(), tfd_relaxed_one_hot_categorical(), tfd_sample_distribution(), tfd_sinh_arcsinh(), tfd_skellam(), tfd_spherical_uniform(), tfd_student_t_process(), tfd_student_t(), tfd_transformed_distribution(), tfd_triangular(), tfd_truncated_cauchy(), tfd_truncated_normal(), tfd_uniform(), tfd_variational_gaussian_process(), tfd_vector_diffeomixture(), tfd_vector_exponential_diag(), tfd_vector_exponential_linear_operator(), tfd_vector_laplace_diag(), tfd_vector_laplace_linear_operator(), tfd_vector_sinh_arcsinh_diag(), tfd_von_mises_fisher(), tfd_von_mises(), tfd_weibull(), tfd_wishart_linear_operator(), tfd_wishart_tri_l(), tfd_wishart(), tfd_zipf()