1 | #ifndef _theplu_yat_statistics_utility_ |
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2 | #define _theplu_yat_statistics_utility_ |
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3 | |
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4 | // $Id: utility.h 1470 2008-09-02 17:46:36Z peter $ |
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5 | |
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6 | /* |
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7 | Copyright (C) 2004 Jari Häkkinen, Peter Johansson |
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8 | Copyright (C) 2005 Peter Johansson |
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9 | Copyright (C) 2006 Jari Häkkinen, Peter Johansson, Markus Ringnér |
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10 | Copyright (C) 2007 Jari Häkkinen, Peter Johansson |
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11 | Copyright (C) 2008 Peter Johansson |
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12 | |
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13 | This file is part of the yat library, http://dev.thep.lu.se/yat |
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14 | |
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15 | The yat library is free software; you can redistribute it and/or |
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16 | modify it under the terms of the GNU General Public License as |
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17 | published by the Free Software Foundation; either version 2 of the |
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18 | License, or (at your option) any later version. |
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19 | |
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20 | The yat library is distributed in the hope that it will be useful, |
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21 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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22 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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23 | General Public License for more details. |
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24 | |
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25 | You should have received a copy of the GNU General Public License |
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26 | along with this program; if not, write to the Free Software |
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27 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA |
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28 | 02111-1307, USA. |
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29 | */ |
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30 | |
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31 | #include "Percentiler.h" |
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32 | |
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33 | #include "yat/classifier/DataLookupWeighted1D.h" |
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34 | #include "yat/classifier/Target.h" |
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35 | #include "yat/utility/VectorBase.h" |
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36 | #include "yat/utility/yat_assert.h" |
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37 | |
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38 | #include <algorithm> |
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39 | #include <cmath> |
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40 | #include <stdexcept> |
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41 | #include <vector> |
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42 | |
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43 | #include <gsl/gsl_statistics_double.h> |
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44 | |
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45 | namespace theplu { |
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46 | namespace yat { |
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47 | namespace statistics { |
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48 | |
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49 | /** |
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50 | \brief 50th percentile |
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51 | @see Percentiler |
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52 | */ |
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53 | template <class T> |
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54 | double median(T first, T last, const bool sorted=false); |
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55 | |
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56 | /** |
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57 | \see Percentiler |
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58 | */ |
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59 | template <class T> |
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60 | double percentile(T first, T last, double p, bool sorted=false); |
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61 | |
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62 | /** |
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63 | Adding a range [\a first, \a last) into an object of type T. The |
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64 | requirements for the type T is to have an add(double, bool, double) |
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65 | function. |
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66 | */ |
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67 | template <typename T, typename ForwardIterator> |
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68 | void add(T& o, ForwardIterator first, ForwardIterator last, |
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69 | const classifier::Target& target) |
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70 | { |
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71 | for (size_t i=0; first!=last; ++i, ++first) |
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72 | o.add(utility::iterator_traits<ForwardIterator>().data(first), |
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73 | target.binary(i), |
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74 | utility::iterator_traits<ForwardIterator>().weight(first)); |
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75 | } |
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76 | |
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77 | /// |
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78 | /// Calculates the probability to get \a k or smaller from a |
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79 | /// hypergeometric distribution with parameters \a n1 \a n2 \a |
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80 | /// t. Hypergeomtric situation you get in the following situation: |
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81 | /// Let there be \a n1 ways for a "good" selection and \a n2 ways |
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82 | /// for a "bad" selection out of a total of possibilities. Take \a |
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83 | /// t samples without replacement and \a k of those are "good" |
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84 | /// samples. \a k will follow a hypergeomtric distribution. |
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85 | /// |
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86 | /// @return cumulative hypergeomtric distribution functions P(k). |
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87 | /// |
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88 | double cdf_hypergeometric_P(unsigned int k, unsigned int n1, |
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89 | unsigned int n2, unsigned int t); |
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90 | |
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91 | |
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92 | /** |
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93 | \brief one-sided p-value |
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94 | |
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95 | This function uses the t-distribution to calculate the one-sided |
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96 | p-value. Given that the true correlation is zero (Null |
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97 | hypothesis) the estimated correlation, r, after a transformation |
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98 | is t-distributed: |
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99 | |
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100 | \f$ \sqrt{(n-2)} \frac{r}{\sqrt{(1-r^2)}} \in t(n-2) \f$ |
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101 | |
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102 | \return Probability that correlation is larger than \a r by |
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103 | chance when having \a n samples. |
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104 | */ |
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105 | double pearson_p_value(double r, unsigned int n); |
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106 | |
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107 | /// |
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108 | /// @brief Computes the kurtosis of the data in a vector. |
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109 | /// |
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110 | /// The kurtosis measures how sharply peaked a distribution is, |
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111 | /// relative to its width. The kurtosis is normalized to zero for a |
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112 | /// gaussian distribution. |
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113 | /// |
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114 | double kurtosis(const utility::VectorBase&); |
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115 | |
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116 | |
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117 | /// |
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118 | /// @brief Median absolute deviation from median |
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119 | /// |
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120 | /// Function is non-mutable function |
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121 | /// |
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122 | template <class T> |
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123 | double mad(T first, T last, const bool sorted=false) |
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124 | { |
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125 | double m = median(first, last, sorted); |
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126 | std::vector<double> ad; |
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127 | ad.reserve(std::distance(first, last)); |
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128 | for( ; first!=last; ++first) |
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129 | ad.push_back(fabs(*first-m)); |
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130 | std::sort(ad.begin(), ad.end()); |
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131 | return median(ad.begin(), ad.end(), true); |
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132 | } |
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133 | |
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134 | |
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135 | /// |
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136 | /// Median is defined to be value in the middle. If number of values |
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137 | /// is even median is the average of the two middle values. the |
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138 | /// median value is given by p equal to 50. If \a sorted is false |
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139 | /// (default), the range is copied, the copy is sorted, and then |
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140 | /// used to calculate the median. |
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141 | /// |
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142 | /// Function is a non-mutable function, i.e., \a first and \a last |
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143 | /// can be const_iterators. |
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144 | /// |
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145 | /// Requirements: T should be an iterator over a range of doubles (or |
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146 | /// any type being convertable to double). |
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147 | /// |
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148 | /// @return median of range |
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149 | /// |
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150 | template <class T> |
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151 | double median(T first, T last, const bool sorted=false) |
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152 | { return percentile2(first, last, 50.0, sorted); } |
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153 | |
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154 | /** |
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155 | The percentile is determined by the \a p, a number between 0 and |
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156 | 100. The percentile is found by interpolation, using the formula |
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157 | \f$ percentile = (1 - \delta) x_i + \delta x_{i+1} \f$ where \a |
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158 | p is floor\f$((n - 1)p/100)\f$ and \f$ \delta \f$ is \f$ |
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159 | (n-1)p/100 - i \f$.Thus the minimum value of the vector is given |
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160 | by p equal to zero, the maximum is given by p equal to 100 and |
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161 | the median value is given by p equal to 50. If @a sorted |
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162 | is false (default), the vector is copied, the copy is sorted, |
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163 | and then used to calculate the median. |
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164 | |
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165 | Function is a non-mutable function, i.e., \a first and \a last |
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166 | can be const_iterators. |
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167 | |
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168 | Requirements: T should be an iterator over a range of doubles (or |
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169 | any type being convertable to double). |
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170 | |
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171 | @return \a p'th percentile of range |
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172 | |
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173 | \deprecated percentile2 will replace this function in the future |
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174 | |
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175 | \note the definition of percentile used here is not identical to |
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176 | that one used in percentile2 and Percentile. The difference is |
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177 | smaller for large ranges. |
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178 | */ |
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179 | template <class RandomAccessIterator> |
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180 | double percentile(RandomAccessIterator first, RandomAccessIterator last, |
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181 | double p, bool sorted=false) |
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182 | { |
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183 | // range is one value only is a special case |
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184 | if (first+1 == last) |
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185 | return utility::iterator_traits<RandomAccessIterator>().data(first); |
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186 | if (sorted) { |
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187 | // have to take care of this special case |
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188 | if (p>=100) |
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189 | return utility::iterator_traits<RandomAccessIterator>().data(--last); |
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190 | double j = p/100 * (std::distance(first,last)-1); |
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191 | int i = static_cast<int>(j); |
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192 | return (1-j+floor(j))*first[i] + (j-floor(j))*first[i+1]; |
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193 | } |
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194 | |
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195 | std::vector<typename std::iterator_traits<RandomAccessIterator>::value_type> |
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196 | v_copy; |
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197 | v_copy.reserve(std::distance(first,last)); |
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198 | std::copy(first, last, std::back_inserter(v_copy)); |
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199 | size_t i = static_cast<size_t>(p/100 * (v_copy.size()-1)); |
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200 | if (i+2 < v_copy.size()) { |
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201 | std::partial_sort(v_copy.begin(), v_copy.begin()+i+2, v_copy.end()); |
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202 | } |
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203 | else |
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204 | std::sort(v_copy.begin(), v_copy.end()); |
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205 | return percentile(v_copy.begin(), v_copy.end(), p, true); |
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206 | } |
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207 | |
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208 | |
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209 | /** |
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210 | \see Percentiler |
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211 | |
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212 | \since new in yat 0.5 |
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213 | */ |
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214 | template <class RandomAccessIterator> |
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215 | double percentile2(RandomAccessIterator first, RandomAccessIterator last, |
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216 | double p, bool sorted=false) |
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217 | { |
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218 | Percentiler percentiler(p, sorted); |
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219 | return percentiler(first, last); |
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220 | } |
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221 | |
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222 | /// |
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223 | /// @brief Computes the skewness of the data in a vector. |
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224 | /// |
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225 | /// The skewness measures the asymmetry of the tails of a |
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226 | /// distribution. |
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227 | /// |
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228 | double skewness(const utility::VectorBase&); |
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229 | |
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230 | }}} // of namespace statistics, yat, and theplu |
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231 | |
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232 | #endif |
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