// 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_CHI_SQUARE_H_ #define ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_ // 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. #include <cassert> #include "absl/base/config.h" 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 #endif // ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_