add missing file

git-svn-id: http://root.cern.ch/svn/root/trunk@17115 27541ba8-7e3a-0410-8455-c3a389f83636

mathcore/inc/Math/PdfFuncMathCore.h

+// @(#)root/mathcore:$Name:  $:$Id: PdfFunc.h,v 1.1 2006/12/07 11:07:03 moneta Exp $
+// Authors: Andras Zsenei & Lorenzo Moneta   06/2005 
+
+/**********************************************************************
+ *                                                                    *
+ * Copyright (c) 2005 , LCG ROOT MathLib Team                         *
+ *                                                                    *
+ *                                                                    *
+ **********************************************************************/
+
+
+
+/**
+
+Probability density functions, cumulative distribution functions 
+and their inverses of the different distributions.
+Whenever possible the conventions followed are those of the
+CRC Concise Encyclopedia of Mathematics, Second Edition
+(or <A HREF="http://mathworld.wolfram.com/">Mathworld</A>).
+By convention the distributions are centered around 0, so for
+example in the case of a Gaussian there is no parameter mu. The
+user must calculate the shift himself if he wishes.
+
+
+@author Created by Andras Zsenei on Wed Nov 17 2004
+
+@defgroup StatFunc Statistical functions
+
+*/
+
+
+
+
+
+
+#ifndef ROOT_Math_PdfFuncMathCore
+#define ROOT_Math_PdfFuncMathCore
+
+
+
+
+namespace ROOT {
+namespace Math {
+
+
+
+  /** @name Probability Density Functions (PDF)
+   *  Probability density functions of various distributions.
+   *  The probability density function returns the probability that 
+   *  the variate has the value x. 
+   *  In statistics the PDF is called also as the frequency function.
+   * 
+   */
+  //@{
+
+  /**
+    
+  Probability density function of the binomial distribution.
+
+  \f[ p(k) = \frac{n!}{k! (n-k)!} p^k (1-p)^{n-k} \f]
+
+  for \f$ 0 \leq k \leq n \f$. For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/BinomialDistribution.html">
+  Mathworld</A>. 
+  
+  @ingroup StatFunc
+
+  */
+
+  double binomial_pdf(unsigned int k, double p, unsigned int n);
+
+
+
+
+  /**
+
+  Probability density function of Breit-Wigner distribution, which is similar, just 
+  a different definition of the parameters, to the Cauchy distribution 
+  (see  #cauchy_pdf )
+
+  \f[ p(x) = \frac{1}{\pi} \frac{\frac{1}{2} \Gamma}{x^2 + (\frac{1}{2} \Gamma)^2} \f]
+
+  
+  @ingroup StatFunc
+
+  */
+
+  double breitwigner_pdf(double x, double gamma, double x0 = 0);
+
+
+
+
+  /**
+
+  Probability density function of the Cauchy distribution which is also
+  called Lorentzian distribution.
+
+  
+  \f[ p(x) = \frac{1}{\pi} \frac{ b }{ (x-m)^2 + b^2} \f]
+
+  For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/CauchyDistribution.html">
+  Mathworld</A>. It is also related to the #breitwigner_pdf which 
+  will call the same implementation.
+  
+  @ingroup StatFunc
+
+  */
+
+  double cauchy_pdf(double x, double b = 1, double x0 = 0);
+
+
+
+
+  /**
+
+  Probability density function of the \f$\chi^2\f$ distribution with \f$r\f$ 
+  degrees of freedom.
+
+  \f[ p_r(x) = \frac{1}{\Gamma(r/2) 2^{r/2}} x^{r/2-1} e^{-x/2} \f]
+
+  for \f$x \geq 0\f$. For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/Chi-SquaredDistribution.html">
+  Mathworld</A>. 
+  
+  @ingroup StatFunc
+
+  */
+
+  double chisquared_pdf(double x, double r, double x0 = 0);
+
+
+
+
+  /**
+
+  Probability density function of the exponential distribution.
+
+  \f[ p(x) = \lambda e^{-\lambda x} \f]
+
+  for x>0. For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/ExponentialDistribution.html">
+  Mathworld</A>. 
+
+  
+  @ingroup StatFunc
+
+  */
+
+  double exponential_pdf(double x, double lambda, double x0 = 0);
+
+
+
+
+  /**
+
+  Probability density function of the F-distribution.
+
+  \f[ p_{n,m}(x) = \frac{\Gamma(\frac{n+m}{2})}{\Gamma(\frac{n}{2}) \Gamma(\frac{m}{2})} n^{n/2} m^{m/2} x^{n/2 -1} (m+nx)^{-(n+m)/2} \f]
+
+  for x>=0. For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/F-Distribution.html">
+  Mathworld</A>. 
+  
+  @ingroup StatFunc
+
+  */
+
+
+  double fdistribution_pdf(double x, double n, double m, double x0 = 0);
+
+
+
+
+  /**
+
+  Probability density function of the gamma distribution.
+
+  \f[ p(x) = {1 \over \Gamma(\alpha) \theta^{\alpha}} x^{\alpha-1} e^{-x/\theta} \f]
+
+  for x>0. For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/GammaDistribution.html">
+  Mathworld</A>. 
+  
+  @ingroup StatFunc
+
+  */
+
+  double gamma_pdf(double x, double alpha, double theta, double x0 = 0);
+
+
+
+
+  /**
+
+  Probability density function of the normal (Gaussian) distribution.
+
+  \f[ p(x) = {1 \over \sqrt{2 \pi \sigma^2}} e^{-x^2 / 2\sigma^2} \f]
+
+  For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/NormalDistribution.html">
+  Mathworld</A>. It can also be evaluated using #normal_pdf which will 
+  call the same implementation. 
+
+  @ingroup StatFunc
+ 
+  */
+
+  double gaussian_pdf(double x, double sigma, double x0 = 0);
+
+
+
+
+
+  /**
+
+  Probability density function of the lognormal distribution.
+
+  \f[ p(x) = {1 \over x \sqrt{2 \pi s^2} } e^{-(\ln{x} - m)^2/2 s^2} \f]
+
+  for x>0. For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/LogNormalDistribution.html">
+  Mathworld</A>. 
+
+  
+  @ingroup StatFunc
+
+  */
+
+  double lognormal_pdf(double x, double m, double s, double x0 = 0);
+
+
+
+
+  /**
+
+  Probability density function of the normal (Gaussian) distribution.
+
+  \f[ p(x) = {1 \over \sqrt{2 \pi \sigma^2}} e^{-x^2 / 2\sigma^2} \f]
+
+  For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/NormalDistribution.html">
+  Mathworld</A>. It can also be evaluated using #gaussian_pdf which will call the same 
+  implementation. 
+
+  @ingroup StatFunc
+ 
+  */
+
+  double normal_pdf(double x, double sigma, double x0 = 0);
+
+
+
+
+  /**
+
+  Probability density function of the Poisson distribution.
+
+  \f[ p(n) = \frac{\mu^n}{n!} e^{- \mu} \f]
+
+  For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/PoissonDistribution.html">
+  Mathworld</A>. 
+  
+  @ingroup StatFunc
+
+  */
+
+  double poisson_pdf(unsigned int n, double mu);
+
+
+
+
+  /**
+
+  Probability density function of Student's t-distribution.
+
+  \f[ p_{r}(x) = \frac{\Gamma(\frac{r+1}{2})}{\sqrt{r \pi}\Gamma(\frac{r}{2})} \left( 1+\frac{x^2}{r}\right)^{-(r+1)/2}  \f]
+
+  for \f$k \geq 0\f$. For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/Studentst-Distribution.html">
+  Mathworld</A>. 
+  
+  @ingroup StatFunc
+
+  */
+
+  double tdistribution_pdf(double x, double r, double x0 = 0);
+
+
+
+
+  /**
+
+  Probability density function of the uniform (flat) distribution.
+
+  \f[ p(x) = {1 \over (b-a)} \f]
+
+  if \f$a \leq x<b\f$ and 0 otherwise. For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/UniformDistribution.html">
+  Mathworld</A>. 
+  
+  @ingroup StatFunc
+
+  */
+
+  double uniform_pdf(double x, double a, double b, double x0 = 0);
+
+
+
+
+
+
+
+
+
+
+} // namespace Math
+} // namespace ROOT
+
+
+
+#endif // ROOT_Math_PdfFunc

mathmore/inc/Math/PdfFuncMathMore.h

+// @(#)root/mathmore:$Name:  $:$Id: ProbFuncMathMore.h,v 1.2 2006/12/06 17:53:47 moneta Exp $
+// 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.             *
+  *                                                                    *
+  **********************************************************************/
+
+/**
+
+Probability density functions, cumulative distribution functions 
+and their inverses of the different distributions.
+Whenever possible the conventions followed are those of the
+CRC Concise Encyclopedia of Mathematics, Second Edition
+(or <A HREF="http://mathworld.wolfram.com/">Mathworld</A>).
+By convention the distributions are centered around 0, so for
+example in the case of a Gaussian there is no parameter mu. The
+user must calculate the shift himself if he wishes.
+
+
+@author Created by Andras Zsenei on Wed Nov 17 2004
+
+@defgroup StatFunc Statistical functions
+
+*/
+
+
+#ifndef ROOT_Math_PdfFuncMathMore
+#define ROOT_Math_PdfFuncMathMore
+
+namespace ROOT {
+namespace Math {
+
+  /** @name Probability Density Functions (PDF)
+   *  Probability density functions of various distributions.
+   *  The probability density function returns the probability that 
+   *  the variate has the value x. 
+   *  In statistics the PDF is called also as the frequency function.
+   *   
+   */
+
+  //@{
+
+  /**
+     
+  Probability density function of the beta distribution.
+  
+  \f[ p(x) = \frac{\Gamma (a + b) } {\Gamma(a)\Gamma(b) } x ^{a-1} (1 - x)^{b-1} \f]
+
+  for \f$0 \leq x \leq 1 \f$. For detailed description see 
+  <A HREF="http://mathworld.wolfram.com/BetaDistribution.html">
+  Mathworld</A>. The implementation used is that of 
+  <A HREF="http://www.gnu.org/software/gsl/manual/html_node/The-Beta-Distribution.html">GSL</A>.
+  
+  @ingroup StatFunc
+
+  */
+
+  double beta_pdf(double x, double a, double b);
+
+
+
+   /**
+
+   Probability density function of the Landau distribution.
+   
+   \f[  p(x) = \frac{1}{2 \pi i}\int_{c-i\infty}^{c+i\infty} e^{x s + s \log{s}} ds\f]
+   
+   Where s = (x-x0)/sigma. For detailed description see 
+   <A HREF="http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/g110/top.html">
+   CERNLIB</A>. 
+   
+   @ingroup StatFunc
+   
+   */
+
+   double landau_pdf(double x, double sigma = 1, double x0 = 0.); 
+
+  /**
+
+  Multinomial distribution probability density function
+
+  http://mathworld.wolfram.com/MultinomialDistribution.html
+
+  */
+
+  //double multinomial_pdf(const size_t k, const double p[], const unsigned int n[]);
+
+
+  //@}
+
+
+} // namespace Math
+} // namespace ROOT
+
+
+#endif // ROOT_Math_ProbFuncMathMore