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0001 // @(#)root/mathmore:$Id$ 0002 // Authors: L. Moneta, A. Zsenei 08/2005 0003 0004 0005 0006 /********************************************************************** 0007 * * 0008 * Copyright (c) 2004 ROOT Foundation, CERN/PH-SFT * 0009 * * 0010 * This library is free software; you can redistribute it and/or * 0011 * modify it under the terms of the GNU General Public License * 0012 * as published by the Free Software Foundation; either version 2 * 0013 * of the License, or (at your option) any later version. * 0014 * * 0015 * This library is distributed in the hope that it will be useful, * 0016 * but WITHOUT ANY WARRANTY; without even the implied warranty of * 0017 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * 0018 * General Public License for more details. * 0019 * * 0020 * You should have received a copy of the GNU General Public License * 0021 * along with this library (see file COPYING); if not, write * 0022 * to the Free Software Foundation, Inc., 59 Temple Place, Suite * 0023 * 330, Boston, MA 02111-1307 USA, or contact the author. * 0024 * * 0025 **********************************************************************/ 0026 0027 0028 #ifndef ROOT_Math_QuantFuncMathMore 0029 #define ROOT_Math_QuantFuncMathMore 0030 0031 0032 namespace ROOT { 0033 namespace Math { 0034 0035 0036 0037 /** @defgroup QuantFunc Quantile Functions 0038 * @ingroup StatFunc 0039 * 0040 * Inverse functions of the cumulative distribution functions 0041 * and the inverse of the complement of the cumulative distribution functions 0042 * for various distributions. 0043 * The functions with the extension <em>_quantile</em> calculate the 0044 * inverse of the <em>_cdf</em> function, the 0045 * lower tail integral of the probability density function 0046 * \f$D^{-1}(z)\f$ where 0047 * 0048 * \f[ D(x) = \int_{-\infty}^{x} p(x') dx' \f] 0049 * 0050 * while those with the <em>_quantile_c</em> extension calculate the 0051 * inverse of the <em>_cdf_c</em> functions, the upper tail integral of the probability 0052 * density function \f$D^{-1}(z) \f$ where 0053 * 0054 * \f[ D(x) = \int_{x}^{+\infty} p(x') dx' \f] 0055 * 0056 * The implementation used is that of 0057 * <A HREF="http://www.gnu.org/software/gsl/manual/html_node/Random-Number-Distributions.html">GSL</A>. 0058 * 0059 * <strong>NOTE:</strong> In the old releases (< 5.14) the <em>_quantile</em> functions were called 0060 * <em>_quant_inv</em> and the <em>_quantile_c</em> functions were called 0061 * <em>_prob_inv</em>. 0062 * These names are currently kept for backward compatibility, but 0063 * their usage is deprecated. 0064 */ 0065 0066 /** @name Quantile Functions from MathMore 0067 * The implementation used is that of 0068 * <A HREF="http://www.gnu.org/software/gsl/manual/html_node/Random-Number-Distributions.html">GSL</A>. 0069 */ 0070 0071 //@{ 0072 0073 0074 /** 0075 0076 Inverse (\f$D^{-1}(z)\f$) of the cumulative distribution 0077 function of the upper tail of Student's t-distribution 0078 (#tdistribution_cdf_c). For detailed description see 0079 <A HREF="http://mathworld.wolfram.com/Studentst-Distribution.html"> 0080 Mathworld</A>. The implementation used is that of 0081 <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_19.html#SEC305">GSL</A>. 0082 0083 @ingroup QuantFunc 0084 0085 */ 0086 0087 double tdistribution_quantile_c(double z, double r); 0088 0089 0090 0091 0092 /** 0093 0094 Inverse (\f$D^{-1}(z)\f$) of the cumulative distribution 0095 function of the lower tail of Student's t-distribution 0096 (#tdistribution_cdf). For detailed description see 0097 <A HREF="http://mathworld.wolfram.com/Studentst-Distribution.html"> 0098 Mathworld</A>. The implementation used is that of 0099 <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_19.html#SEC305">GSL</A>. 0100 0101 @ingroup QuantFunc 0102 0103 */ 0104 0105 double tdistribution_quantile(double z, double r); 0106 0107 0108 #ifdef HAVE_OLD_STAT_FUNC 0109 0110 //@} 0111 /** @name Backward compatible functions */ 0112 0113 0114 } 0115 inline double chisquared_quant_inv(double x, double r) { 0116 return chisquared_quantile (x, r ); 0117 } 0118 0119 0120 inline double gamma_quant_inv(double x, double alpha, double theta) { 0121 return gamma_quantile (x, alpha, theta ); 0122 } 0123 0124 inline double tdistribution_prob_inv(double x, double r) { 0125 return tdistribution_quantile_c (x, r ); 0126 } 0127 0128 inline double tdistribution_quant_inv(double x, double r) { 0129 return tdistribution_quantile (x, r ); 0130 } 0131 0132 #endif 0133 0134 0135 } // namespace Math 0136 0137 namespace MathMore { 0138 0139 0140 0141 /** 0142 0143 Re-implementation in MathMore of the Inverse (\f$D^{-1}(z)\f$) of the cumulative distribution 0144 function of the lower tail of the \f$\chi^2\f$ distribution 0145 with \f$r\f$ degrees of freedom (ROOT::Math::chisquared_cdf). For detailed description see 0146 <A HREF="http://mathworld.wolfram.com/Chi-SquaredDistribution.html"> 0147 Mathworld</A>. The implementation used is that of 0148 <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_19.html#SEC303">GSL</A>. 0149 0150 @ingroup QuantFunc 0151 0152 */ 0153 0154 double chisquared_quantile(double z, double r); 0155 0156 0157 0158 0159 /** 0160 0161 Re-implementation in MathMore of the Inverse (\f$D^{-1}(z)\f$) of the cumulative distribution 0162 function of the lower tail of the gamma distribution 0163 (#ROOT::Math::gamma_cdf). For detailed description see 0164 <A HREF="http://mathworld.wolfram.com/GammaDistribution.html"> 0165 Mathworld</A>. The implementation used is that of 0166 <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_19.html#SEC300">GSL</A>. 0167 0168 @ingroup QuantFunc 0169 0170 */ 0171 0172 double gamma_quantile(double z, double alpha, double theta); 0173 0174 0175 0176 } // end namespace MathMore 0177 } // namespace ROOT 0178 0179 0180 0181 #endif // ROOT_Math_QuantFuncMathMore
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