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Reference Guide
Statistical functions from truncated distributions

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 functions Math/StatFunc.h

Functions

double ROOT::Math::landau_xm1 (double x, double xi=1, double x0=0)
 First moment (mean) of the truncated Landau distribution. More...
 
double ROOT::Math::landau_xm2 (double x, double xi=1, double x0=0)
 Second moment of the truncated Landau distribution. More...
 

Function Documentation

◆ landau_xm1()

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
xThe argument \(x\)
xiThe width parameter \(\xi\)
x0The location parameter \(x_0\)

Definition at line 409 of file ProbFuncMathCore.cxx.

◆ 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
xThe argument \(x\)
xiThe width parameter \(\xi\)
x0The location parameter \(x_0\)

Definition at line 489 of file ProbFuncMathCore.cxx.