gum::Chi2 Class Reference

Static math utilities for the chi2 distribution. More...

#include <agrum/base/core/math/chi2.h>

Static Public Member Functions
Static math utilities
static double	probaChi2 (double x, Size df)
	Computes the probability of chi2 value.
static double	criticalValue (double proba, Size df)
	Computes the critical chi2 value for a given confidence probability and number of degrees of freedom.

Private Member Functions
	Chi2 ()=delete

Static Private Member Functions
static double	_probaZValue_ (double z)
	Computes the probability of normal z value.

Detailed Description

Static math utilities for the chi2 distribution.

Definition at line 73 of file chi2.h.

Constructor & Destructor Documentation

Chi2()

gum::Chi2::Chi2 ( )

privatedelete

Member Function Documentation

_probaZValue_()

double gum::Chi2::_probaZValue_ ( double z )

staticprivate

Computes the probability of normal z value.

This code has been written by Gary Perlman.

ALGORITHM Adapted from a polynomial approximation in: Ibbetson D, Algorithm 209 Collected Algorithms of the CACM 1963 p. 616

This routine has six digit accuracy, so it is only useful for absolute z values < 6. For z values >= to 6.0, probaZValue() returns 0.0.

Parameters

z

A value.

Returns

The probability of z.

Definition at line 72 of file chi2.cpp.

                                     {
    double y, x, w;
 
    if (z == 0.0) x = 0.0;
    else {
      y = 0.5 * std::fabs(z);
 
      if (y >= (GUM_Z_MAX * 0.5)) x = 1.0;
      else if (y < 1.0) {
        w = y * y;
        x = ((((((((0.000124818987 * w - 0.001075204047) * w + 0.005198775019) * w - 0.019198292004)
                     * w
                 + 0.059054035642)
                    * w
                - 0.151968751364)
                   * w
               + 0.319152932694)
                  * w
              - 0.531923007300)
                 * w
             + 0.797884560593)
          * y * 2.0;
      } else {
        y -= 2.0;
        x = (((((((((((((-0.000045255659 * y + 0.000152529290) * y - 0.000019538132) * y
                       - 0.000676904986)
                          * y
                      + 0.001390604284)
                         * y
                     - 0.000794620820)
                        * y
                    - 0.002034254874)
                       * y
                   + 0.006549791214)
                      * y
                  - 0.010557625006)
                     * y
                 + 0.011630447319)
                    * y
                - 0.009279453341)
                   * y
               + 0.005353579108)
                  * y
              - 0.002141268741)
                 * y
             + 0.000535310849)
              * y
          + 0.999936657524;
      }
    }
 
    return (z > 0.0 ? ((x + 1.0) * 0.5) : ((1.0 - x) * 0.5));
  }

Referenced by probaChi2().

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criticalValue()

double gum::Chi2::criticalValue ( double proba, Size df )

static

Computes the critical chi2 value for a given confidence probability and number of degrees of freedom.

This code has been written by Gary Perlman.

Parameters

proba	The confidence probability.
df	The number of degrees of freedom.

Returns

The critical chi2 value.

Definition at line 173 of file chi2.cpp.

                                                  {
    double minchisq = 0.0;
    double maxchisq = GUM_CHI_MAX;
    double chisqval;
 
    if (df == 0) return (0.0);
 
    if (proba <= 0.0) return (maxchisq);
    else if (proba >= 1.0) return (0.0);
 
    chisqval = df / std::sqrt(proba); /* fair first value */
 
    while (maxchisq - minchisq > GUM_CHI_EPSILON) {
      if (probaChi2(chisqval, df) < proba) maxchisq = chisqval;
      else minchisq = chisqval;
 
      chisqval = (maxchisq + minchisq) * 0.5;
    }
 
    return (chisqval);
  }

References probaChi2().

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probaChi2()

double gum::Chi2::probaChi2 ( double x, Size df )

static

Computes the probability of chi2 value.

This code has been written by Gary Perlman.

ALGORITHM Compute probability of chi square value. Adapted from: Hill, I. D. and Pike, M. C. Algorithm 299 Collected Algorithms for the CACM 1967 p. 243 Updated for rounding errors based on remark in ACM TOMS June 1985, page 185

Parameters

x	The chi2 value.
df	The number of degrees of freedom.

Returns

The probability of x given df degrees of freedom.

Definition at line 127 of file chi2.cpp.

                                          {
    double a, y = 0, s;
    double e, c, z;
    int    even; /* true if df is an even number */
 
    if ((x <= 0.0) || (df < 1)) return (1.0);
 
    a = 0.5 * x;
 
    even = (2 * (df / 2)) == df;
 
    if (df > 1) y = _gum_ex(-a);
 
    s = (even ? y : (2.0 * _probaZValue_(-std::sqrt(x))));
 
    if (df > 2) {
      x = 0.5 * (df - 1.0);
      z = (even ? 1.0 : 0.5);
 
      if (a > GUM_BIGX) {
        e = (even ? 0.0 : GUM_LOG_SQRT_PI);
        c = std::log(a);
 
        while (z <= x) {
          e = std::log(z) + e;
          s += _gum_ex(c * z - a - e);
          z += 1.0;
        }
 
        return (s);
      } else {
        e = (even ? 1.0 : (GUM_I_SQRT_PI / std::sqrt(a)));
        c = 0.0;
 
        while (z <= x) {
          e = e * (a / z);
          c = c + e;
          z += 1.0;
        }
 
        return (c * y + s);
      }
    } else return (s);
  }

References _probaZValue_().

Referenced by criticalValue().

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The documentation for this class was generated from the following files:

• agrum/base/core/math/chi2.h
• agrum/base/core/math/chi2.cpp