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// Copyright 2022 Jay Gohil, Hans Dembinski // // Distributed under the Boost Software License, version 1.0. // (See accompanying file LICENSE_1_0.txt // or copy at http://www.boost.org/LICENSE_1_0.txt) #ifndef BOOST_HISTOGRAM_UTILITY_WILSON_INTERVAL_HPP #define BOOST_HISTOGRAM_UTILITY_WILSON_INTERVAL_HPP #include #include #include #include namespace boost { namespace histogram { namespace utility { /** Wilson interval. The Wilson score interval is simple to compute, has good coverage. Intervals are automatically bounded between 0 and 1 and never empty. The interval is asymmetric. Wilson, E. B. (1927). "Probable inference, the law of succession, and statistical inference". Journal of the American Statistical Association. 22 (158): 209-212. doi:10.1080/01621459.1927.10502953. JSTOR 2276774. The coverage probability for a random ensemble of fractions is close to the nominal value. Unlike the Clopper-Pearson interval, the Wilson score interval is not conservative. For some values of the fractions, the interval undercovers and overcovers for neighboring values. This is a shared property of all alternatives to the Clopper-Pearson interval. The Wilson score intervals is widely recommended for general use in the literature. For a review of the literature, see R. D. Cousins, K. E. Hymes, J. Tucker, Nucl. Instrum. Meth. A 612 (2010) 388-398. */ template class wilson_interval : public binomial_proportion_interval { public: using value_type = typename wilson_interval::value_type; using interval_type = typename wilson_interval::interval_type; /** Construct Wilson interval computer. @param d Number of standard deviations for the interval. The default value 1 corresponds to a confidence level of 68 %. Both `deviation` and `confidence_level` objects can be used to initialize the interval. */ explicit wilson_interval(deviation d = deviation{1.0}) noexcept : z_{static_cast(d)} {} using binomial_proportion_interval::operator(); /** Compute interval for given number of successes and failures. @param successes Number of successful trials. @param failures Number of failed trials. */ interval_type operator()(value_type successes, value_type failures) const noexcept override { // See https://en.wikipedia.org/wiki/ // Binomial_proportion_confidence_interval // #Wilson_score_interval // We make sure calculation is done in single precision if value_type is float // by converting all literals to value_type. Double literals in the equation // would turn intermediate values to double. const value_type half{0.5}, quarter{0.25}, zsq{z_ * z_}; const value_type total = successes + failures; const value_type minv = 1 / (total + zsq); const value_type t1 = (successes + half * zsq) * minv; const value_type t2 = z_ * minv * std::sqrt(successes * failures / total + quarter * zsq); return {t1 - t2, t1 + t2}; } private: value_type z_; }; } // namespace utility } // namespace histogram } // namespace boost #endif