ceph/src/boost/boost/math/distributions/fisher_f.hpp

   1 // Copyright John Maddock 2006.
   2
   3 // Use, modification and distribution are subject to the
   4 // Boost Software License, Version 1.0.
   5 // (See accompanying file LICENSE_1_0.txt
   6 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   7
   8 #ifndef BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP
   9 #define BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP
  10
  11 #include <boost/math/distributions/fwd.hpp>
  12 #include <boost/math/special_functions/beta.hpp> // for incomplete beta.
  13 #include <boost/math/distributions/complement.hpp> // complements
  14 #include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
  15 #include <boost/math/special_functions/fpclassify.hpp>
  16
  17 #include <utility>
  18
  19 namespace boost{ namespace math{
  20
  21 template <class RealType = double, class Policy = policies::policy<> >
  22 class fisher_f_distribution
  23 {
  24 public:
  25    typedef RealType value_type;
  26    typedef Policy policy_type;
  27
  28    fisher_f_distribution(const RealType& i, const RealType& j) : m_df1(i), m_df2(j)
  29    {
  30       static const char* function = "fisher_f_distribution<%1%>::fisher_f_distribution";
  31       RealType result;
  32       detail::check_df(
  33          function, m_df1, &result, Policy());
  34       detail::check_df(
  35          function, m_df2, &result, Policy());
  36    } // fisher_f_distribution
  37
  38    RealType degrees_of_freedom1()const
  39    {
  40       return m_df1;
  41    }
  42    RealType degrees_of_freedom2()const
  43    {
  44       return m_df2;
  45    }
  46
  47 private:
  48    //
  49    // Data members:
  50    //
  51    RealType m_df1;  // degrees of freedom are a real number.
  52    RealType m_df2;  // degrees of freedom are a real number.
  53 };
  54
  55 typedef fisher_f_distribution<double> fisher_f;
  56
  57 template <class RealType, class Policy>
  58 inline const std::pair<RealType, RealType> range(const fisher_f_distribution<RealType, Policy>& /*dist*/)
  59 { // Range of permissible values for random variable x.
  60    using boost::math::tools::max_value;
  61    return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
  62 }
  63
  64 template <class RealType, class Policy>
  65 inline const std::pair<RealType, RealType> support(const fisher_f_distribution<RealType, Policy>& /*dist*/)
  66 { // Range of supported values for random variable x.
  67    // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
  68    using boost::math::tools::max_value;
  69    return std::pair<RealType, RealType>(static_cast<RealType>(0),  max_value<RealType>());
  70 }
  71
  72 template <class RealType, class Policy>
  73 RealType pdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x)
  74 {
  75    BOOST_MATH_STD_USING  // for ADL of std functions
  76    RealType df1 = dist.degrees_of_freedom1();
  77    RealType df2 = dist.degrees_of_freedom2();
  78    // Error check:
  79    RealType error_result = 0;
  80    static const char* function = "boost::math::pdf(fisher_f_distribution<%1%> const&, %1%)";
  81    if(false == (detail::check_df(
  82          function, df1, &error_result, Policy())
  83          && detail::check_df(
  84          function, df2, &error_result, Policy())))
  85       return error_result;
  86
  87    if((x < 0) || !(boost::math::isfinite)(x))
  88    {
  89       return policies::raise_domain_error<RealType>(
  90          function, "Random variable parameter was %1%, but must be > 0 !", x, Policy());
  91    }
  92
  93    if(x == 0)
  94    {
  95       // special cases:
  96       if(df1 < 2)
  97          return policies::raise_overflow_error<RealType>(
  98             function, 0, Policy());
  99       else if(df1 == 2)
 100          return 1;
 101       else
 102          return 0;
 103    }
 104
 105    //
 106    // You reach this formula by direct differentiation of the
 107    // cdf expressed in terms of the incomplete beta.
 108    //
 109    // There are two versions so we don't pass a value of z
 110    // that is very close to 1 to ibeta_derivative: for some values
 111    // of df1 and df2, all the change takes place in this area.
 112    //
 113    RealType v1x = df1 * x;
 114    RealType result;
 115    if(v1x > df2)
 116    {
 117       result = (df2 * df1) / ((df2 + v1x) * (df2 + v1x));
 118       result *= ibeta_derivative(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy());
 119    }
 120    else
 121    {
 122       result = df2 + df1 * x;
 123       result = (result * df1 - x * df1 * df1) / (result * result);
 124       result *= ibeta_derivative(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
 125    }
 126    return result;
 127 } // pdf
 128
 129 template <class RealType, class Policy>
 130 inline RealType cdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x)
 131 {
 132    static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)";
 133    RealType df1 = dist.degrees_of_freedom1();
 134    RealType df2 = dist.degrees_of_freedom2();
 135    // Error check:
 136    RealType error_result = 0;
 137    if(false == detail::check_df(
 138          function, df1, &error_result, Policy())
 139          && detail::check_df(
 140          function, df2, &error_result, Policy()))
 141       return error_result;
 142
 143    if((x < 0) || !(boost::math::isfinite)(x))
 144    {
 145       return policies::raise_domain_error<RealType>(
 146          function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy());
 147    }
 148
 149    RealType v1x = df1 * x;
 150    //
 151    // There are two equivalent formulas used here, the aim is
 152    // to prevent the final argument to the incomplete beta
 153    // from being too close to 1: for some values of df1 and df2
 154    // the rate of change can be arbitrarily large in this area,
 155    // whilst the value we're passing will have lost information
 156    // content as a result of being 0.999999something.  Better
 157    // to switch things around so we're passing 1-z instead.
 158    //
 159    return v1x > df2
 160       ? boost::math::ibetac(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
 161       : boost::math::ibeta(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
 162 } // cdf
 163
 164 template <class RealType, class Policy>
 165 inline RealType quantile(const fisher_f_distribution<RealType, Policy>& dist, const RealType& p)
 166 {
 167    static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)";
 168    RealType df1 = dist.degrees_of_freedom1();
 169    RealType df2 = dist.degrees_of_freedom2();
 170    // Error check:
 171    RealType error_result = 0;
 172    if(false == (detail::check_df(
 173             function, df1, &error_result, Policy())
 174          && detail::check_df(
 175             function, df2, &error_result, Policy())
 176          && detail::check_probability(
 177             function, p, &error_result, Policy())))
 178       return error_result;
 179
 180    // With optimizations turned on, gcc wrongly warns about y being used
 181    // uninitializated unless we initialize it to something:
 182    RealType x, y(0);
 183
 184    x = boost::math::ibeta_inv(df1 / 2, df2 / 2, p, &y, Policy());
 185
 186    return df2 * x / (df1 * y);
 187 } // quantile
 188
 189 template <class RealType, class Policy>
 190 inline RealType cdf(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
 191 {
 192    static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)";
 193    RealType df1 = c.dist.degrees_of_freedom1();
 194    RealType df2 = c.dist.degrees_of_freedom2();
 195    RealType x = c.param;
 196    // Error check:
 197    RealType error_result = 0;
 198    if(false == detail::check_df(
 199          function, df1, &error_result, Policy())
 200          && detail::check_df(
 201          function, df2, &error_result, Policy()))
 202       return error_result;
 203
 204    if((x < 0) || !(boost::math::isfinite)(x))
 205    {
 206       return policies::raise_domain_error<RealType>(
 207          function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy());
 208    }
 209
 210    RealType v1x = df1 * x;
 211    //
 212    // There are two equivalent formulas used here, the aim is
 213    // to prevent the final argument to the incomplete beta
 214    // from being too close to 1: for some values of df1 and df2
 215    // the rate of change can be arbitrarily large in this area,
 216    // whilst the value we're passing will have lost information
 217    // content as a result of being 0.999999something.  Better
 218    // to switch things around so we're passing 1-z instead.
 219    //
 220    return v1x > df2
 221       ? boost::math::ibeta(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
 222       : boost::math::ibetac(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
 223 }
 224
 225 template <class RealType, class Policy>
 226 inline RealType quantile(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
 227 {
 228    static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)";
 229    RealType df1 = c.dist.degrees_of_freedom1();
 230    RealType df2 = c.dist.degrees_of_freedom2();
 231    RealType p = c.param;
 232    // Error check:
 233    RealType error_result = 0;
 234    if(false == (detail::check_df(
 235             function, df1, &error_result, Policy())
 236          && detail::check_df(
 237             function, df2, &error_result, Policy())
 238          && detail::check_probability(
 239             function, p, &error_result, Policy())))
 240       return error_result;
 241
 242    RealType x, y;
 243
 244    x = boost::math::ibetac_inv(df1 / 2, df2 / 2, p, &y, Policy());
 245
 246    return df2 * x / (df1 * y);
 247 }
 248
 249 template <class RealType, class Policy>
 250 inline RealType mean(const fisher_f_distribution<RealType, Policy>& dist)
 251 { // Mean of F distribution = v.
 252    static const char* function = "boost::math::mean(fisher_f_distribution<%1%> const&)";
 253    RealType df1 = dist.degrees_of_freedom1();
 254    RealType df2 = dist.degrees_of_freedom2();
 255    // Error check:
 256    RealType error_result = 0;
 257    if(false == detail::check_df(
 258             function, df1, &error_result, Policy())
 259          && detail::check_df(
 260             function, df2, &error_result, Policy()))
 261       return error_result;
 262    if(df2 <= 2)
 263    {
 264       return policies::raise_domain_error<RealType>(
 265          function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mean.", df2, Policy());
 266    }
 267    return df2 / (df2 - 2);
 268 } // mean
 269
 270 template <class RealType, class Policy>
 271 inline RealType variance(const fisher_f_distribution<RealType, Policy>& dist)
 272 { // Variance of F distribution.
 273    static const char* function = "boost::math::variance(fisher_f_distribution<%1%> const&)";
 274    RealType df1 = dist.degrees_of_freedom1();
 275    RealType df2 = dist.degrees_of_freedom2();
 276    // Error check:
 277    RealType error_result = 0;
 278    if(false == detail::check_df(
 279             function, df1, &error_result, Policy())
 280          && detail::check_df(
 281             function, df2, &error_result, Policy()))
 282       return error_result;
 283    if(df2 <= 4)
 284    {
 285       return policies::raise_domain_error<RealType>(
 286          function, "Second degree of freedom was %1% but must be > 4 in order for the distribution to have a valid variance.", df2, Policy());
 287    }
 288    return 2 * df2 * df2 * (df1 + df2 - 2) / (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4));
 289 } // variance
 290
 291 template <class RealType, class Policy>
 292 inline RealType mode(const fisher_f_distribution<RealType, Policy>& dist)
 293 {
 294    static const char* function = "boost::math::mode(fisher_f_distribution<%1%> const&)";
 295    RealType df1 = dist.degrees_of_freedom1();
 296    RealType df2 = dist.degrees_of_freedom2();
 297    // Error check:
 298    RealType error_result = 0;
 299    if(false == detail::check_df(
 300             function, df1, &error_result, Policy())
 301          && detail::check_df(
 302             function, df2, &error_result, Policy()))
 303       return error_result;
 304    if(df2 <= 2)
 305    {
 306       return policies::raise_domain_error<RealType>(
 307          function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mode.", df2, Policy());
 308    }
 309    return df2 * (df1 - 2) / (df1 * (df2 + 2));
 310 }
 311
 312 //template <class RealType, class Policy>
 313 //inline RealType median(const fisher_f_distribution<RealType, Policy>& dist)
 314 //{ // Median of Fisher F distribution is not defined.
 315 //  return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN());
 316 //  } // median
 317
 318 // Now implemented via quantile(half) in derived accessors.
 319
 320 template <class RealType, class Policy>
 321 inline RealType skewness(const fisher_f_distribution<RealType, Policy>& dist)
 322 {
 323    static const char* function = "boost::math::skewness(fisher_f_distribution<%1%> const&)";
 324    BOOST_MATH_STD_USING // ADL of std names
 325    // See http://mathworld.wolfram.com/F-Distribution.html
 326    RealType df1 = dist.degrees_of_freedom1();
 327    RealType df2 = dist.degrees_of_freedom2();
 328    // Error check:
 329    RealType error_result = 0;
 330    if(false == detail::check_df(
 331             function, df1, &error_result, Policy())
 332          && detail::check_df(
 333             function, df2, &error_result, Policy()))
 334       return error_result;
 335    if(df2 <= 6)
 336    {
 337       return policies::raise_domain_error<RealType>(
 338          function, "Second degree of freedom was %1% but must be > 6 in order for the distribution to have a skewness.", df2, Policy());
 339    }
 340    return 2 * (df2 + 2 * df1 - 2) * sqrt((2 * df2 - 8) / (df1 * (df2 + df1 - 2))) / (df2 - 6);
 341 }
 342
 343 template <class RealType, class Policy>
 344 RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist);
 345
 346 template <class RealType, class Policy>
 347 inline RealType kurtosis(const fisher_f_distribution<RealType, Policy>& dist)
 348 {
 349    return 3 + kurtosis_excess(dist);
 350 }
 351
 352 template <class RealType, class Policy>
 353 inline RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist)
 354 {
 355    static const char* function = "boost::math::kurtosis_excess(fisher_f_distribution<%1%> const&)";
 356    // See http://mathworld.wolfram.com/F-Distribution.html
 357    RealType df1 = dist.degrees_of_freedom1();
 358    RealType df2 = dist.degrees_of_freedom2();
 359    // Error check:
 360    RealType error_result = 0;
 361    if(false == detail::check_df(
 362             function, df1, &error_result, Policy())
 363          && detail::check_df(
 364             function, df2, &error_result, Policy()))
 365       return error_result;
 366    if(df2 <= 8)
 367    {
 368       return policies::raise_domain_error<RealType>(
 369          function, "Second degree of freedom was %1% but must be > 8 in order for the distribution to have a kutosis.", df2, Policy());
 370    }
 371    RealType df2_2 = df2 * df2;
 372    RealType df1_2 = df1 * df1;
 373    RealType n = -16 + 20 * df2 - 8 * df2_2 + df2_2 * df2 + 44 * df1 - 32 * df2 * df1 + 5 * df2_2 * df1 - 22 * df1_2 + 5 * df2 * df1_2;
 374    n *= 12;
 375    RealType d = df1 * (df2 - 6) * (df2 - 8) * (df1 + df2 - 2);
 376    return n / d;
 377 }
 378
 379 } // namespace math
 380 } // namespace boost
 381
 382 // This include must be at the end, *after* the accessors
 383 // for this distribution have been defined, in order to
 384 // keep compilers that support two-phase lookup happy.
 385 #include <boost/math/distributions/detail/derived_accessors.hpp>
 386
 387 #endif // BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP