// @(#)root/mathmore:$Id$ // Authors: L. Moneta, A. Zsenei 08/2005 /********************************************************************** * * * Copyright (c) 2004 ROOT Foundation, CERN/PH-SFT * * * * This library is free software; you can redistribute it and/or * * modify it under the terms of the GNU General Public License * * as published by the Free Software Foundation; either version 2 * * of the License, or (at your option) any later version. * * * * This library is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * * General Public License for more details. * * * * You should have received a copy of the GNU General Public License * * along with this library (see file COPYING); if not, write * * to the Free Software Foundation, Inc., 59 Temple Place, Suite * * 330, Boston, MA 02111-1307 USA, or contact the author. * * * **********************************************************************/ #ifndef ROOT_Math_QuantFuncMathMore #define ROOT_Math_QuantFuncMathMore namespace ROOT { namespace Math { /** @defgroup QuantFunc Quantile Functions * @ingroup StatFunc * * Inverse functions of the cumulative distribution functions * and the inverse of the complement of the cumulative distribution functions * for various distributions. * The functions with the extension _quantile calculate the * inverse of the _cdf function, the * lower tail integral of the probability density function * \f$D^{-1}(z)\f$ where * * \f[ D(x) = \int_{-\infty}^{x} p(x') dx' \f] * * while those with the _quantile_c extension calculate the * inverse of the _cdf_c functions, the upper tail integral of the probability * density function \f$D^{-1}(z) \f$ where * * \f[ D(x) = \int_{x}^{+\infty} p(x') dx' \f] * * The implementation used is that of * GSL. * * NOTE: In the old releases (< 5.14) the _quantile functions were called * _quant_inv and the _quantile_c functions were called * _prob_inv. * These names are currently kept for backward compatibility, but * their usage is deprecated. */ /** @name Quantile Functions from MathMore * The implementation used is that of * GSL. */ //@{ /** Inverse (\f$D^{-1}(z)\f$) of the cumulative distribution function of the upper tail of Student's t-distribution (#tdistribution_cdf_c). For detailed description see Mathworld. The implementation used is that of GSL. @ingroup QuantFunc */ double tdistribution_quantile_c(double z, double r); /** Inverse (\f$D^{-1}(z)\f$) of the cumulative distribution function of the lower tail of Student's t-distribution (#tdistribution_cdf). For detailed description see Mathworld. The implementation used is that of GSL. @ingroup QuantFunc */ double tdistribution_quantile(double z, double r); #ifdef HAVE_OLD_STAT_FUNC //@} /** @name Backward compatible functions */ } inline double chisquared_quant_inv(double x, double r) { return chisquared_quantile (x, r ); } inline double gamma_quant_inv(double x, double alpha, double theta) { return gamma_quantile (x, alpha, theta ); } inline double tdistribution_prob_inv(double x, double r) { return tdistribution_quantile_c (x, r ); } inline double tdistribution_quant_inv(double x, double r) { return tdistribution_quantile (x, r ); } #endif } // namespace Math namespace MathMore { /** Re-implementation in MathMore of the Inverse (\f$D^{-1}(z)\f$) of the cumulative distribution function of the lower tail of the \f$\chi^2\f$ distribution with \f$r\f$ degrees of freedom (#chisquared_cdf). For detailed description see Mathworld. The implementation used is that of GSL. @ingroup QuantFunc */ double chisquared_quantile(double z, double r); /** Re-implementation in MathMore of the Inverse (\f$D^{-1}(z)\f$) of the cumulative distribution function of the lower tail of the gamma distribution (#gamma_cdf). For detailed description see Mathworld. The implementation used is that of GSL. @ingroup QuantFunc */ double gamma_quantile(double z, double alpha, double theta); } // end namespace MathMore } // namespace ROOT #endif // ROOT_Math_QuantFuncMathMore