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// -*- C++ -*-
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// Copyright (C) 2005, 2006, 2009 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the terms
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// of the GNU General Public License as published by the Free Software
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// Foundation; either version 3, or (at your option) any later
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// version.
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// This library is distributed in the hope that it will be useful, but
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// WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// General Public License for more details.
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// You should have received a copy of the GNU General Public License
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// along with this library; see the file COPYING3. If not see
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// <http://www.gnu.org/licenses/>.
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// Copyright (C) 2004 Ami Tavory and Vladimir Dreizin, IBM-HRL.
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// Permission to use, copy, modify, sell, and distribute this software
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// is hereby granted without fee, provided that the above copyright
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// notice appears in all copies, and that both that copyright notice
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// and this permission notice appear in supporting documentation. None
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// of the above authors, nor IBM Haifa Research Laboratories, make any
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// representation about the suitability of this software for any
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// purpose. It is provided "as is" without express or implied
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// warranty.
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/**
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* @file sample_mean_confidence_checker.hpp
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* Contains a function for checking the confidence of a sample mean
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*/
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#ifndef PB_DS_SAMPLE_MEAN_CONFIDENCE_CHECKER_HPP
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#define PB_DS_SAMPLE_MEAN_CONFIDENCE_CHECKER_HPP
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#include <list>
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#include <numeric>
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#include <math.h>
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namespace __gnu_pbds
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{
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namespace test
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{
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namespace detail
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{
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/*
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* Checks that a sample mean sm is in the relative interval
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* relative_interval of a true mean (assuming i.i.d. samples),
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* given a sample variance sv taken over num_samples samples,
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* with confidence ~ 0.95.
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*
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* See "Probability, Random Variables, and Stochastic Processes"
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* (Third edition) Athanasios Papoulis, Chapter 9.
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*/
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template<typename Value_Type>
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bool
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sample_mean_confidence_checker(Value_Type sm, Value_Type sv,
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std::size_t num_samples,
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double relative_interval)
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{
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enum
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{
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// Ensures that the student-t distribution is approximately normal.
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min_num_samples = 30
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};
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if (num_samples < min_num_samples)
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return (false);
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// This is z_u (normal-dist percentile) for u = 0.975.
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const Value_Type z = 1.976;
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return (sv / ::sqrt(double(num_samples)) <= relative_interval * sm / z);
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}
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} // namespace detail
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} // namespace test
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} // namespace __gnu_pbds
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#endif
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