| // 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. | |
| // The chi-square statistic. | |
| // | |
| // Useful for evaluating if `D` independent random variables are behaving as | |
| // expected, or if two distributions are similar. (`D` is the degrees of | |
| // freedom). | |
| // | |
| // Each bucket should have an expected count of 10 or more for the chi square to | |
| // be meaningful. | |
| namespace absl { | |
| ABSL_NAMESPACE_BEGIN | |
| namespace random_internal { | |
| constexpr const char kChiSquared[] = "chi-squared"; | |
| // Returns the measured chi square value, using a single expected value. This | |
| // assumes that the values in [begin, end) are uniformly distributed. | |
| template <typename Iterator> | |
| double ChiSquareWithExpected(Iterator begin, Iterator end, double expected) { | |
| // Compute the sum and the number of buckets. | |
| assert(expected >= 10); // require at least 10 samples per bucket. | |
| double chi_square = 0; | |
| for (auto it = begin; it != end; it++) { | |
| double d = static_cast<double>(*it) - expected; | |
| chi_square += d * d; | |
| } | |
| chi_square = chi_square / expected; | |
| return chi_square; | |
| } | |
| // Returns the measured chi square value, taking the actual value of each bucket | |
| // from the first set of iterators, and the expected value of each bucket from | |
| // the second set of iterators. | |
| template <typename Iterator, typename Expected> | |
| double ChiSquare(Iterator it, Iterator end, Expected eit, Expected eend) { | |
| double chi_square = 0; | |
| for (; it != end && eit != eend; ++it, ++eit) { | |
| if (*it > 0) { | |
| assert(*eit > 0); | |
| } | |
| double e = static_cast<double>(*eit); | |
| double d = static_cast<double>(*it - *eit); | |
| if (d != 0) { | |
| assert(e > 0); | |
| chi_square += (d * d) / e; | |
| } | |
| } | |
| assert(it == end && eit == eend); | |
| return chi_square; | |
| } | |
| // ====================================================================== | |
| // The following methods can be used for an arbitrary significance level. | |
| // | |
| // Calculates critical chi-square values to produce the given p-value using a | |
| // bisection search for a value within epsilon, relying on the monotonicity of | |
| // ChiSquarePValue(). | |
| double ChiSquareValue(int dof, double p); | |
| // Calculates the p-value (probability) of a given chi-square value. | |
| double ChiSquarePValue(double chi_square, int dof); | |
| } // namespace random_internal | |
| ABSL_NAMESPACE_END | |
| } // namespace absl | |