fj_char_max_blom.h File Reference

Blom-corrected plotting position for the characteristic maximum. More...

#include <cmath>
#include <functional>
#include <limits>
#include "line/api/fj/fj_types.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for fj_char_max_blom.h:

Go to the source code of this file.

Classes
struct	line::fj::FJCharMaxBlomResult< T >
	[mK, lo, hi] of fj_char_max_blom; lo and hi are NaN below K = 5. More...

Namespaces
namespace	line
namespace	line::fj

Functions
template<class T>
FJCharMaxBlomResult< T >	line::fj::fj_char_max_blom (unsigned K, const std::function< T(const T &)> &Finv=std::function< T(const T &)>(), const T &alpha=num_traits< T >::from_double(0.4886), const T &beta=num_traits< T >::from_double(0.3140))
	Blom-corrected plotting position for the characteristic maximum.

Detailed Description

Blom-corrected plotting position for the characteristic maximum.

Templated port of matlab/src/api/fj/fj_char_max_blom.m.

m_K = F^-1( (K - alpha) / (K - alpha - beta + 1) )

which for alpha = beta = 0 falls back on the naive K/(K+1). The survey quotes alpha = 0.4886 and beta = 0.3140, which are the defaults. For the standard normal the position is bracketed without any inversion, for K >= 5, by

sqrt(2 ln K - ln ln K - 3) < m_K < sqrt(2 ln K - ln ln K).

Definition in file fj_char_max_blom.h.