Statistical functions from truncated distributions
[Statistical functions]


Functions

double ROOT::Math::landau_xm1 (double x, double xi=1, double x0=0)
double ROOT::Math::landau_xm2 (double x, double xi=1, double x0=0)

Detailed Description

Statistical functions for the truncated distributions. Examples of such functions are the first or the second momentum of the truncated distribution. In the case of the Landau, first and second momentum functions are provided for the Landau distribution truncated only on the right side. These functions are defined in the header file Math/ProbFunc.h or in the global one including all statistical dunctions Math/StatFunc.h

Function Documentation

double ROOT::Math::landau_xm1 ( double  x,
double  xi = 1,
double  x0 = 0 
)

First moment (mean) of the truncated Landau distribution.

\[ \frac{1}{D (x)} \int_{-\infty}^{x} t\, p(t) d t \]

where $p(x)$ is the Landau distribution and $D(x)$ its cumulative distribution function.

For detailed description see K.S. Kölbig and B. Schorr, A program package for the Landau distribution, Computer Phys. Comm. 31 (1984) 97-111 [Erratum-ibid. 178 (2008) 972]. The same algorithms as in CERNLIB (XM1LAN) is used

Parameters:
x The argument $x$
xi The width parameter $\xi$
x0 The location parameter $x_0$

Definition at line 369 of file ProbFuncMathCore.cxx.

References exp(), log(), p1(), p2(), p3(), p4(), and u.

Referenced by G__G__MathCore_170_0_59(), G__setup_memfuncROOTcLcLMath(), and ROOT::Math::landau_xm2().

double ROOT::Math::landau_xm2 ( double  x,
double  xi = 1,
double  x0 = 0 
)

Second moment of the truncated Landau distribution.

\[ \frac{1}{D (x)} \int_{-\infty}^{x} t^2\, p(t) d t \]

where $p(x)$ is the Landau distribution and $D(x)$ its cumulative distribution function.

For detailed description see K.S. Kölbig and B. Schorr, A program package for the Landau distribution, Computer Phys. Comm. 31 (1984) 97-111 [Erratum-ibid. 178 (2008) 972]. The same algorithms as in CERNLIB (XM1LAN) is used

Parameters:
x The argument $x$
xi The width parameter $\xi$
x0 The location parameter $x_0$

Definition at line 448 of file ProbFuncMathCore.cxx.

References exp(), ROOT::Math::landau_xm1(), log(), p1(), p2(), p3(), p4(), and u.

Referenced by G__G__MathCore_170_0_60(), and G__setup_memfuncROOTcLcLMath().

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