1 | // Copyright Thijs van den Berg, 2008.
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2 | // Copyright John Maddock 2008.
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3 | // Copyright Paul A. Bristow 2008, 2014.
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4 |
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5 | // Use, modification and distribution are subject to the
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6 | // Boost Software License, Version 1.0. (See accompanying file
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7 | // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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8 |
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9 | // This module implements the Laplace distribution.
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10 | // Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource.
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11 | // http://mathworld.wolfram.com/LaplaceDistribution.html
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12 | // http://en.wikipedia.org/wiki/Laplace_distribution
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13 | //
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14 | // Abramowitz and Stegun 1972, p 930
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15 | // http://www.math.sfu.ca/~cbm/aands/page_930.htm
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16 |
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17 | #ifndef BOOST_STATS_LAPLACE_HPP
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18 | #define BOOST_STATS_LAPLACE_HPP
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19 |
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20 | #include <boost/math/distributions/detail/common_error_handling.hpp>
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21 | #include <boost/math/distributions/complement.hpp>
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22 | #include <boost/math/constants/constants.hpp>
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23 | #include <limits>
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24 |
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25 | namespace boost{ namespace math{
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26 |
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27 | template <class RealType = double, class Policy = policies::policy<> >
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28 | class laplace_distribution
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29 | {
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30 | public:
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31 | // ----------------------------------
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32 | // public Types
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33 | // ----------------------------------
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34 | typedef RealType value_type;
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35 | typedef Policy policy_type;
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36 |
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37 | // ----------------------------------
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38 | // Constructor(s)
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39 | // ----------------------------------
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40 | laplace_distribution(RealType l_location = 0, RealType l_scale = 1)
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41 | : m_location(l_location), m_scale(l_scale)
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42 | {
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43 | RealType result;
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44 | check_parameters("boost::math::laplace_distribution<%1%>::laplace_distribution()", &result);
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45 | }
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46 |
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47 |
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48 | // ----------------------------------
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49 | // Public functions
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50 | // ----------------------------------
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51 |
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52 | RealType location() const
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53 | {
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54 | return m_location;
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55 | }
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56 |
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57 | RealType scale() const
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58 | {
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59 | return m_scale;
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60 | }
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61 |
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62 | bool check_parameters(const char* function, RealType* result) const
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63 | {
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64 | if(false == detail::check_scale(function, m_scale, result, Policy())) return false;
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65 | if(false == detail::check_location(function, m_location, result, Policy())) return false;
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66 | return true;
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67 | }
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68 |
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69 | private:
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70 | RealType m_location;
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71 | RealType m_scale;
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72 | }; // class laplace_distribution
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73 |
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74 | //
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75 | // Convenient type synonym for double
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76 | typedef laplace_distribution<double> laplace;
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77 |
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78 | //
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79 | // Non member functions
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80 | template <class RealType, class Policy>
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81 | inline const std::pair<RealType, RealType> range(const laplace_distribution<RealType, Policy>&)
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82 | {
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83 | using boost::math::tools::max_value;
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84 | return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
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85 | }
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86 |
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87 | template <class RealType, class Policy>
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88 | inline const std::pair<RealType, RealType> support(const laplace_distribution<RealType, Policy>&)
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89 | {
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90 | using boost::math::tools::max_value;
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91 | return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
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92 | }
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93 |
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94 | template <class RealType, class Policy>
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95 | inline RealType pdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x)
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96 | {
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97 | BOOST_MATH_STD_USING // for ADL of std functions
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98 |
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99 | // Checking function argument
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100 | RealType result = 0;
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101 | const char* function = "boost::math::pdf(const laplace_distribution<%1%>&, %1%))";
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102 |
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103 | // Check scale and location.
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104 | if (false == dist.check_parameters(function, &result)) return result;
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105 | // Special pdf values.
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106 | if((boost::math::isinf)(x))
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107 | {
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108 | return 0; // pdf + and - infinity is zero.
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109 | }
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110 | if (false == detail::check_x(function, x, &result, Policy())) return result;
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111 |
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112 | // General case
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113 | RealType scale( dist.scale() );
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114 | RealType location( dist.location() );
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115 |
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116 | RealType exponent = x - location;
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117 | if (exponent>0) exponent = -exponent;
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118 | exponent /= scale;
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119 |
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120 | result = exp(exponent);
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121 | result /= 2 * scale;
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122 |
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123 | return result;
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124 | } // pdf
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125 |
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126 | template <class RealType, class Policy>
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127 | inline RealType cdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x)
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128 | {
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129 | BOOST_MATH_STD_USING // For ADL of std functions.
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130 |
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131 | RealType result = 0;
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132 | // Checking function argument.
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133 | const char* function = "boost::math::cdf(const laplace_distribution<%1%>&, %1%)";
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134 | // Check scale and location.
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135 | if (false == dist.check_parameters(function, &result)) return result;
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136 |
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137 | // Special cdf values:
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138 | if((boost::math::isinf)(x))
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139 | {
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140 | if(x < 0) return 0; // -infinity.
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141 | return 1; // + infinity.
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142 | }
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143 | if (false == detail::check_x(function, x, &result, Policy())) return result;
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144 |
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145 | // General cdf values
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146 | RealType scale( dist.scale() );
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147 | RealType location( dist.location() );
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148 |
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149 | if (x < location)
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150 | {
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151 | result = exp( (x-location)/scale )/2;
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152 | }
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153 | else
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154 | {
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155 | result = 1 - exp( (location-x)/scale )/2;
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156 | }
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157 | return result;
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158 | } // cdf
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159 |
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160 |
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161 | template <class RealType, class Policy>
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162 | inline RealType quantile(const laplace_distribution<RealType, Policy>& dist, const RealType& p)
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163 | {
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164 | BOOST_MATH_STD_USING // for ADL of std functions.
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165 |
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166 | // Checking function argument
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167 | RealType result = 0;
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168 | const char* function = "boost::math::quantile(const laplace_distribution<%1%>&, %1%)";
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169 | if (false == dist.check_parameters(function, &result)) return result;
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170 | if(false == detail::check_probability(function, p, &result, Policy())) return result;
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171 |
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172 | // Extreme values of p:
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173 | if(p == 0)
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174 | {
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175 | result = policies::raise_overflow_error<RealType>(function,
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176 | "probability parameter is 0, but must be > 0!", Policy());
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177 | return -result; // -std::numeric_limits<RealType>::infinity();
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178 | }
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179 |
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180 | if(p == 1)
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181 | {
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182 | result = policies::raise_overflow_error<RealType>(function,
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183 | "probability parameter is 1, but must be < 1!", Policy());
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184 | return result; // std::numeric_limits<RealType>::infinity();
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185 | }
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186 | // Calculate Quantile
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187 | RealType scale( dist.scale() );
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188 | RealType location( dist.location() );
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189 |
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190 | if (p - 0.5 < 0.0)
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191 | result = location + scale*log( static_cast<RealType>(p*2) );
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192 | else
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193 | result = location - scale*log( static_cast<RealType>(-p*2 + 2) );
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194 |
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195 | return result;
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196 | } // quantile
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197 |
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198 |
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199 | template <class RealType, class Policy>
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200 | inline RealType cdf(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c)
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201 | {
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202 | // Calculate complement of cdf.
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203 | BOOST_MATH_STD_USING // for ADL of std functions
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204 |
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205 | RealType scale = c.dist.scale();
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206 | RealType location = c.dist.location();
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207 | RealType x = c.param;
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208 | RealType result = 0;
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209 |
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210 | // Checking function argument.
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211 | const char* function = "boost::math::cdf(const complemented2_type<laplace_distribution<%1%>, %1%>&)";
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212 |
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213 | // Check scale and location.
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214 | //if(false == detail::check_scale(function, scale, result, Policy())) return false;
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215 | //if(false == detail::check_location(function, location, result, Policy())) return false;
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216 | if (false == c.dist.check_parameters(function, &result)) return result;
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217 |
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218 | // Special cdf values.
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219 | if((boost::math::isinf)(x))
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220 | {
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221 | if(x < 0) return 1; // cdf complement -infinity is unity.
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222 | return 0; // cdf complement +infinity is zero.
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223 | }
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224 | if(false == detail::check_x(function, x, &result, Policy()))return result;
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225 |
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226 | // Cdf interval value.
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227 | if (-x < -location)
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228 | {
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229 | result = exp( (-x+location)/scale )/2;
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230 | }
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231 | else
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232 | {
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233 | result = 1 - exp( (-location+x)/scale )/2;
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234 | }
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235 | return result;
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236 | } // cdf complement
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237 |
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238 |
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239 | template <class RealType, class Policy>
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240 | inline RealType quantile(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c)
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241 | {
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242 | BOOST_MATH_STD_USING // for ADL of std functions.
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243 |
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244 | // Calculate quantile.
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245 | RealType scale = c.dist.scale();
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246 | RealType location = c.dist.location();
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247 | RealType q = c.param;
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248 | RealType result = 0;
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249 |
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250 | // Checking function argument.
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251 | const char* function = "quantile(const complemented2_type<laplace_distribution<%1%>, %1%>&)";
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252 | if (false == c.dist.check_parameters(function, &result)) return result;
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253 |
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254 | // Extreme values.
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255 | if(q == 0)
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256 | {
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257 | return std::numeric_limits<RealType>::infinity();
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258 | }
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259 | if(q == 1)
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260 | {
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261 | return -std::numeric_limits<RealType>::infinity();
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262 | }
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263 | if(false == detail::check_probability(function, q, &result, Policy())) return result;
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264 |
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265 | if (0.5 - q < 0.0)
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266 | result = location + scale*log( static_cast<RealType>(-q*2 + 2) );
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267 | else
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268 | result = location - scale*log( static_cast<RealType>(q*2) );
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269 |
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270 |
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271 | return result;
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272 | } // quantile
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273 |
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274 | template <class RealType, class Policy>
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275 | inline RealType mean(const laplace_distribution<RealType, Policy>& dist)
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276 | {
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277 | return dist.location();
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278 | }
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279 |
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280 | template <class RealType, class Policy>
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281 | inline RealType standard_deviation(const laplace_distribution<RealType, Policy>& dist)
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282 | {
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283 | return constants::root_two<RealType>() * dist.scale();
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284 | }
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285 |
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286 | template <class RealType, class Policy>
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287 | inline RealType mode(const laplace_distribution<RealType, Policy>& dist)
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288 | {
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289 | return dist.location();
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290 | }
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291 |
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292 | template <class RealType, class Policy>
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293 | inline RealType median(const laplace_distribution<RealType, Policy>& dist)
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294 | {
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295 | return dist.location();
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296 | }
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297 |
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298 | template <class RealType, class Policy>
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299 | inline RealType skewness(const laplace_distribution<RealType, Policy>& /*dist*/)
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300 | {
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301 | return 0;
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302 | }
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303 |
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304 | template <class RealType, class Policy>
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305 | inline RealType kurtosis(const laplace_distribution<RealType, Policy>& /*dist*/)
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306 | {
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307 | return 6;
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308 | }
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309 |
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310 | template <class RealType, class Policy>
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311 | inline RealType kurtosis_excess(const laplace_distribution<RealType, Policy>& /*dist*/)
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312 | {
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313 | return 3;
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314 | }
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315 |
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316 | } // namespace math
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317 | } // namespace boost
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318 |
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319 | // This include must be at the end, *after* the accessors
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320 | // for this distribution have been defined, in order to
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321 | // keep compilers that support two-phase lookup happy.
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322 | #include <boost/math/distributions/detail/derived_accessors.hpp>
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323 |
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324 | #endif // BOOST_STATS_LAPLACE_HPP
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325 |
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326 |
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