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_CHI_SQUARE_H_
16 #define ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
17
18 // The chi-square statistic.
19 //
20 // Useful for evaluating if `D` independent random variables are behaving as
21 // expected, or if two distributions are similar. (`D` is the degrees of
22 // freedom).
23 //
24 // Each bucket should have an expected count of 10 or more for the chi square to
25 // be meaningful.
26
27 #include <cassert>
28
29 #include "absl/base/config.h"
30
31 namespace absl {
32 ABSL_NAMESPACE_BEGIN
33 namespace random_internal {
34
35 constexpr const char kChiSquared[] = "chi-squared";
36
37 // Returns the measured chi square value, using a single expected value. This
38 // assumes that the values in [begin, end) are uniformly distributed.
39 template <typename Iterator>
ChiSquareWithExpected(Iterator begin,Iterator end,double expected)40 double ChiSquareWithExpected(Iterator begin, Iterator end, double expected) {
41 // Compute the sum and the number of buckets.
42 assert(expected >= 10); // require at least 10 samples per bucket.
43 double chi_square = 0;
44 for (auto it = begin; it != end; it++) {
45 double d = static_cast<double>(*it) - expected;
46 chi_square += d * d;
47 }
48 chi_square = chi_square / expected;
49 return chi_square;
50 }
51
52 // Returns the measured chi square value, taking the actual value of each bucket
53 // from the first set of iterators, and the expected value of each bucket from
54 // the second set of iterators.
55 template <typename Iterator, typename Expected>
ChiSquare(Iterator it,Iterator end,Expected eit,Expected eend)56 double ChiSquare(Iterator it, Iterator end, Expected eit, Expected eend) {
57 double chi_square = 0;
58 for (; it != end && eit != eend; ++it, ++eit) {
59 if (*it > 0) {
60 assert(*eit > 0);
61 }
62 double e = static_cast<double>(*eit);
63 double d = static_cast<double>(*it - *eit);
64 if (d != 0) {
65 assert(e > 0);
66 chi_square += (d * d) / e;
67 }
68 }
69 assert(it == end && eit == eend);
70 return chi_square;
71 }
72
73 // ======================================================================
74 // The following methods can be used for an arbitrary significance level.
75 //
76
77 // Calculates critical chi-square values to produce the given p-value using a
78 // bisection search for a value within epsilon, relying on the monotonicity of
79 // ChiSquarePValue().
80 double ChiSquareValue(int dof, double p);
81
82 // Calculates the p-value (probability) of a given chi-square value.
83 double ChiSquarePValue(double chi_square, int dof);
84
85 } // namespace random_internal
86 ABSL_NAMESPACE_END
87 } // namespace absl
88
89 #endif // ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
90