1 // Copyright 2017 The Abseil Authors. 2 // 3 // Licensed under the Apache License, Version 2.0 (the "License"); 4 // you may not use this file except in compliance with the License. 5 // You may obtain a copy of the License at 6 // 7 // https://www.apache.org/licenses/LICENSE-2.0 8 // 9 // Unless required by applicable law or agreed to in writing, software 10 // distributed under the License is distributed on an "AS IS" BASIS, 11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 // See the License for the specific language governing permissions and 13 // limitations under the License. 14 15 #ifndef ABSL_RANDOM_INTERNAL_DISTRIBUTION_TEST_UTIL_H_ 16 #define ABSL_RANDOM_INTERNAL_DISTRIBUTION_TEST_UTIL_H_ 17 18 #include <cstddef> 19 #include <iostream> 20 #include <vector> 21 22 #include "absl/strings/string_view.h" 23 #include "absl/types/span.h" 24 25 // NOTE: The functions in this file are test only, and are should not be used in 26 // non-test code. 27 28 namespace absl { 29 ABSL_NAMESPACE_BEGIN 30 namespace random_internal { 31 32 // http://webspace.ship.edu/pgmarr/Geo441/Lectures/Lec%205%20-%20Normality%20Testing.pdf 33 34 // Compute the 1st to 4th standard moments: 35 // mean, variance, skewness, and kurtosis. 36 // http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm 37 struct DistributionMoments { 38 size_t n = 0; 39 double mean = 0.0; 40 double variance = 0.0; 41 double skewness = 0.0; 42 double kurtosis = 0.0; 43 }; 44 DistributionMoments ComputeDistributionMoments( 45 absl::Span<const double> data_points); 46 47 std::ostream& operator<<(std::ostream& os, const DistributionMoments& moments); 48 49 // Computes the Z-score for a set of data with the given distribution moments 50 // compared against `expected_mean`. 51 double ZScore(double expected_mean, const DistributionMoments& moments); 52 53 // Returns the probability of success required for a single trial to ensure that 54 // after `num_trials` trials, the probability of at least one failure is no more 55 // than `p_fail`. 56 double RequiredSuccessProbability(double p_fail, int num_trials); 57 58 // Computes the maximum distance from the mean tolerable, for Z-Tests that are 59 // expected to pass with `acceptance_probability`. Will terminate if the 60 // resulting tolerance is zero (due to passing in 0.0 for 61 // `acceptance_probability` or rounding errors). 62 // 63 // For example, 64 // MaxErrorTolerance(0.001) = 0.0 65 // MaxErrorTolerance(0.5) = ~0.47 66 // MaxErrorTolerance(1.0) = inf 67 double MaxErrorTolerance(double acceptance_probability); 68 69 // Approximation to inverse of the Error Function in double precision. 70 // (http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf) 71 double erfinv(double x); 72 73 // Beta(p, q) = Gamma(p) * Gamma(q) / Gamma(p+q) 74 double beta(double p, double q); 75 76 // The inverse of the normal survival function. 77 double InverseNormalSurvival(double x); 78 79 // Returns whether actual is "near" expected, based on the bound. 80 bool Near(absl::string_view msg, double actual, double expected, double bound); 81 82 // Implements the incomplete regularized beta function, AS63, BETAIN. 83 // https://www.jstor.org/stable/2346797 84 // 85 // BetaIncomplete(x, p, q), where 86 // `x` is the value of the upper limit 87 // `p` is beta parameter p, `q` is beta parameter q. 88 // 89 // NOTE: This is a test-only function which is only accurate to within, at most, 90 // 1e-13 of the actual value. 91 // 92 double BetaIncomplete(double x, double p, double q); 93 94 // Implements the inverse of the incomplete regularized beta function, AS109, 95 // XINBTA. 96 // https://www.jstor.org/stable/2346798 97 // https://www.jstor.org/stable/2346887 98 // 99 // BetaIncompleteInv(p, q, beta, alhpa) 100 // `p` is beta parameter p, `q` is beta parameter q. 101 // `alpha` is the value of the lower tail area. 102 // 103 // NOTE: This is a test-only function and, when successful, is only accurate to 104 // within ~1e-6 of the actual value; there are some cases where it diverges from 105 // the actual value by much more than that. The function uses Newton's method, 106 // and thus the runtime is highly variable. 107 double BetaIncompleteInv(double p, double q, double alpha); 108 109 } // namespace random_internal 110 ABSL_NAMESPACE_END 111 } // namespace absl 112 113 #endif // ABSL_RANDOM_INTERNAL_DISTRIBUTION_TEST_UTIL_H_ 114