# Module: tfp.substrates.numpy.stats

Statistical functions.

## Functions

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

`assign_moving_mean_variance(...)`: Compute one update to the exponentially weighted moving mean and variance.

`auto_correlation(...)`: Auto correlation along one axis.

`brier_decomposition(...)`: Decompose the Brier score into uncertainty, resolution, and reliability.

`brier_score(...)`: Compute Brier score for a probabilistic prediction.

`cholesky_covariance(...)`: Cholesky factor of the covariance matrix of vector-variate random samples.

`correlation(...)`: Sample correlation (Pearson) between observations indexed by `event_axis`.

`count_integers(...)`: Counts the number of occurrences of each value in an integer array `arr`.

`covariance(...)`: Sample covariance between observations indexed by `event_axis`.

`cumulative_variance(...)`: Cumulative estimates of variance.

`expected_calibration_error(...)`: Compute the Expected Calibration Error (ECE).

`expected_calibration_error_quantiles(...)`: Expected calibration error via `quantiles(exp(pred_log_prob),num_buckets)`.

`find_bins(...)`: Bin values into discrete intervals.

`histogram(...)`: Count how often `x` falls in intervals defined by `edges`.

`iterative_mergesort(...)`: Non-recusive mergesort that counts exchanges.

`kendalls_tau(...)`: Computes Kendall's Tau for two ordered lists.

`lexicographical_indirect_sort(...)`: Sorts by primary, then by secondary returning the indices.

`log_average_probs(...)`: Computes `log(average(to_probs(logits)))` in a numerically stable manner.

`log_loomean_exp(...)`: Computes the log-leave-one-out-mean of `exp(logx)`.

`log_loosum_exp(...)`: Computes the log-leave-one-out-sum of `exp(logx)`.

`log_soomean_exp(...)`: Computes the log-swap-one-out-mean of `exp(logx)`.

`log_soosum_exp(...)`: Computes the log-swap-one-out-sum of `exp(logx)`.

`moving_mean_variance_zero_debiased(...)`: Compute zero debiased versions of `moving_mean` and `moving_variance`.

`percentile(...)`: Compute the `q`-th percentile(s) of `x`.

`quantile_auc(...)`: Calculate ranking stats AUROC and AUPRC.

`quantiles(...)`: Compute quantiles of `x` along `axis`.

`stddev(...)`: Estimate standard deviation using samples.

`variance(...)`: Estimate variance using samples.

`windowed_mean(...)`: Windowed estimates of mean.

`windowed_variance(...)`: Windowed estimates of variance.

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