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// -*- C++ -*-
// Copyright (C) 2005-2018 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the terms
// of the GNU General Public License as published by the Free Software
// Foundation; either version 3, or (at your option) any later
// version.
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with this library; see the file COPYING3. If not see
// <http://www.gnu.org/licenses/>.
// Copyright (C) 2004 Ami Tavory and Vladimir Dreizin, IBM-HRL.
// Permission to use, copy, modify, sell, and distribute this software
// is hereby granted without fee, provided that the above copyright
// notice appears in all copies, and that both that copyright notice
// and this permission notice appear in supporting documentation. None
// of the above authors, nor IBM Haifa Research Laboratories, make any
// representation about the suitability of this software for any
// purpose. It is provided "as is" without express or implied
// warranty.
/**
* @file sample_mean_confidence_checker.hpp
* Contains a function for checking the confidence of a sample mean
*/
#ifndef PB_DS_SAMPLE_MEAN_CONFIDENCE_CHECKER_HPP
#define PB_DS_SAMPLE_MEAN_CONFIDENCE_CHECKER_HPP
#include <list>
#include <numeric>
#include <math.h>
namespace __gnu_pbds
{
namespace test
{
namespace detail
{
/*
* Checks that a sample mean sm is in the relative interval
* relative_interval of a true mean (assuming i.i.d. samples),
* given a sample variance sv taken over num_samples samples,
* with confidence ~ 0.95.
*
* See "Probability, Random Variables, and Stochastic Processes"
* (Third edition) Athanasios Papoulis, Chapter 9.
*/
template<typename Value_Type>
bool
sample_mean_confidence_checker(Value_Type sm, Value_Type sv,
std::size_t num_samples,
double relative_interval)
{
enum
{
// Ensures that the student-t distribution is approximately normal.
min_num_samples = 30
};
if (num_samples < min_num_samples)
return (false);
// This is z_u (normal-dist percentile) for u = 0.975.
const Value_Type z = 1.976;
return (sv / ::sqrt(double(num_samples)) <= relative_interval * sm / z);
}
} // namespace detail
} // namespace test
} // namespace __gnu_pbds
#endif
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