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+// Copyright 2017 The Abseil Authors.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef ABSL_RANDOM_INTERNAL_DISTRIBUTION_TEST_UTIL_H_
+#define ABSL_RANDOM_INTERNAL_DISTRIBUTION_TEST_UTIL_H_
+
+#include <cstddef>
+#include <iostream>
+#include <vector>
+
+#include "absl/strings/string_view.h"
+#include "absl/types/span.h"
+
+// NOTE: The functions in this file are test only, and are should not be used in
+// non-test code.
+
+namespace absl {
+namespace random_internal {
+
+// http://webspace.ship.edu/pgmarr/Geo441/Lectures/Lec%205%20-%20Normality%20Testing.pdf
+
+// Compute the 1st to 4th standard moments:
+// mean, variance, skewness, and kurtosis.
+// http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm
+struct DistributionMoments {
+ size_t n = 0;
+ double mean = 0.0;
+ double variance = 0.0;
+ double skewness = 0.0;
+ double kurtosis = 0.0;
+};
+DistributionMoments ComputeDistributionMoments(
+ absl::Span<const double> data_points);
+
+std::ostream& operator<<(std::ostream& os, const DistributionMoments& moments);
+
+// Computes the Z-score for a set of data with the given distribution moments
+// compared against `expected_mean`.
+double ZScore(double expected_mean, const DistributionMoments& moments);
+
+// Returns the probability of success required for a single trial to ensure that
+// after `num_trials` trials, the probability of at least one failure is no more
+// than `p_fail`.
+double RequiredSuccessProbability(double p_fail, int num_trials);
+
+// Computes the maximum distance from the mean tolerable, for Z-Tests that are
+// expected to pass with `acceptance_probability`. Will terminate if the
+// resulting tolerance is zero (due to passing in 0.0 for
+// `acceptance_probability` or rounding errors).
+//
+// For example,
+// MaxErrorTolerance(0.001) = 0.0
+// MaxErrorTolerance(0.5) = ~0.47
+// MaxErrorTolerance(1.0) = inf
+double MaxErrorTolerance(double acceptance_probability);
+
+// Approximation to inverse of the Error Function in double precision.
+// (http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf)
+double erfinv(double x);
+
+// Beta(p, q) = Gamma(p) * Gamma(q) / Gamma(p+q)
+double beta(double p, double q);
+
+// The inverse of the normal survival function.
+double InverseNormalSurvival(double x);
+
+// Returns whether actual is "near" expected, based on the bound.
+bool Near(absl::string_view msg, double actual, double expected, double bound);
+
+// Implements the incomplete regularized beta function, AS63, BETAIN.
+// https://www.jstor.org/stable/2346797
+//
+// BetaIncomplete(x, p, q), where
+// `x` is the value of the upper limit
+// `p` is beta parameter p, `q` is beta parameter q.
+//
+// NOTE: This is a test-only function which is only accurate to within, at most,
+// 1e-13 of the actual value.
+//
+double BetaIncomplete(double x, double p, double q);
+
+// Implements the inverse of the incomplete regularized beta function, AS109,
+// XINBTA.
+// https://www.jstor.org/stable/2346798
+// https://www.jstor.org/stable/2346887
+//
+// BetaIncompleteInv(p, q, beta, alhpa)
+// `p` is beta parameter p, `q` is beta parameter q.
+// `alpha` is the value of the lower tail area.
+//
+// NOTE: This is a test-only function and, when successful, is only accurate to
+// within ~1e-6 of the actual value; there are some cases where it diverges from
+// the actual value by much more than that. The function uses Newton's method,
+// and thus the runtime is highly variable.
+double BetaIncompleteInv(double p, double q, double alpha);
+
+} // namespace random_internal
+} // namespace absl
+
+#endif // ABSL_RANDOM_INTERNAL_DISTRIBUTION_TEST_UTIL_H_