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 dunctions Math/StatFunc.h

Collaboration diagram for Statistical functions from truncated distributions:

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

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 409 of file ProbFuncMathCore.cxx.

Referenced by 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 489 of file ProbFuncMathCore.cxx.