sample_mean_confidence_checker.hpp   [plain text]

// -*- C++ -*-

// Copyright (C) 2005, 2006 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
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// version.

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// General Public License for more details.

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// Copyright (C) 2004 Ami Tavory and Vladimir Dreizin, IBM-HRL.

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// is hereby granted without fee, provided that the above copyright
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/**
 * @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 pb_ds
{
  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 pb_ds

#endif