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