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Diffstat (limited to 'absl/random/internal/distribution_test_util.h')
| -rw-r--r-- | absl/random/internal/distribution_test_util.h | 111 |
1 files changed, 111 insertions, 0 deletions
diff --git a/absl/random/internal/distribution_test_util.h b/absl/random/internal/distribution_test_util.h new file mode 100644 index 00000000..b5ba49fa --- /dev/null +++ b/absl/random/internal/distribution_test_util.h @@ -0,0 +1,111 @@ +// 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_ |