random/internal/chi_square.h

0001 // Copyright 2017 The Abseil Authors.
0002 //
0003 // Licensed under the Apache License, Version 2.0 (the "License");
0004 // you may not use this file except in compliance with the License.
0005 // You may obtain a copy of the License at
0006 //
0007 //      https://www.apache.org/licenses/LICENSE-2.0
0008 //
0009 // Unless required by applicable law or agreed to in writing, software
0010 // distributed under the License is distributed on an "AS IS" BASIS,
0011 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
0012 // See the License for the specific language governing permissions and
0013 // limitations under the License.
0014
0015 #ifndef ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
0016 #define ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
0017
0018 // The chi-square statistic.
0019 //
0020 // Useful for evaluating if `D` independent random variables are behaving as
0021 // expected, or if two distributions are similar.  (`D` is the degrees of
0022 // freedom).
0023 //
0024 // Each bucket should have an expected count of 10 or more for the chi square to
0025 // be meaningful.
0026
0027 #include <cassert>
0028
0029 #include "absl/base/config.h"
0030
0031 namespace absl {
0032 ABSL_NAMESPACE_BEGIN
0033 namespace random_internal {
0034
0035 constexpr const char kChiSquared[] = "chi-squared";
0036
0037 // Returns the measured chi square value, using a single expected value.  This
0038 // assumes that the values in [begin, end) are uniformly distributed.
0039 template <typename Iterator>
0040 double ChiSquareWithExpected(Iterator begin, Iterator end, double expected) {
0041   // Compute the sum and the number of buckets.
0042   assert(expected >= 10);  // require at least 10 samples per bucket.
0043   double chi_square = 0;
0044   for (auto it = begin; it != end; it++) {
0045     double d = static_cast<double>(*it) - expected;
0046     chi_square += d * d;
0047   }
0048   chi_square = chi_square / expected;
0049   return chi_square;
0050 }
0051
0052 // Returns the measured chi square value, taking the actual value of each bucket
0053 // from the first set of iterators, and the expected value of each bucket from
0054 // the second set of iterators.
0055 template <typename Iterator, typename Expected>
0056 double ChiSquare(Iterator it, Iterator end, Expected eit, Expected eend) {
0057   double chi_square = 0;
0058   for (; it != end && eit != eend; ++it, ++eit) {
0059     if (*it > 0) {
0060       assert(*eit > 0);
0061     }
0062     double e = static_cast<double>(*eit);
0063     double d = static_cast<double>(*it - *eit);
0064     if (d != 0) {
0065       assert(e > 0);
0066       chi_square += (d * d) / e;
0067     }
0068   }
0069   assert(it == end && eit == eend);
0070   return chi_square;
0071 }
0072
0073 // ======================================================================
0074 // The following methods can be used for an arbitrary significance level.
0075 //
0076
0077 // Calculates critical chi-square values to produce the given p-value using a
0078 // bisection search for a value within epsilon, relying on the monotonicity of
0079 // ChiSquarePValue().
0080 double ChiSquareValue(int dof, double p);
0081
0082 // Calculates the p-value (probability) of a given chi-square value.
0083 double ChiSquarePValue(double chi_square, int dof);
0084
0085 }  // namespace random_internal
0086 ABSL_NAMESPACE_END
0087 }  // namespace absl
0088
0089 #endif  // ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_