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// 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>
namespace absl {
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
} // namespace absl
#endif // ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
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