ChisqProb (LCSim 3.1.7 API)

java.lang.Object
- org.lcsim.math.chisq.ChisqProb

```
public class ChisqProb
extends Object
```
A utility class to return the probability that a value of chi-squared x measured for a system with n degrees of freedom would be exceeded by chance. Based on routines in the book "Numerical Recipes: The Art of Scientific Computing".

Version:

$Id: ChisqProb.java,v 1.1.1.1 2010/11/30 21:32:00 jeremy Exp $

Author:

Norman Graf

Constructor Summary

Constructors
Constructor and Description

ChisqProb()

Constructors
Constructor and Description
`ChisqProb()`

Method Summary

Methods
Modifier and Type	Method and Description
`static double`	`gammln(double x)` Returns the logarithm of the Gamma function of x, for x>0.
`static double`	`gammp(double a, double x)` Returns the incomplete gamma function P(a, x).
`static double`	`gammq(double a, double x)` Returns the incomplete gamma function Q(a, x)= 1 - P(a, x).
`static double`	`gcf(double a, double x)` Returns the incomplete gamma function Q(a, x) evaluated by its continued fraction representation.
`static double`	`gser(double a, double x)` Returns the incomplete gamma function P(a, x) evaluated by its series representation.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - ChisqProb
```
public ChisqProb()
```
- Method Detail
  - gammp
```
public static double gammp(double a,
           double x)
```
    Returns the incomplete gamma function P(a, x).
    
    P(a,x) � g(a,x)
    G(a)
    � 1
    G(a)
    x
    �
    �
    0
    e^{- t} t^{a - 1} dt
    
    This is the probability that the observed chi-square for a correct model should be less than a value of chi-square.
    
    Parameters:
    a - the number of degrees of freedom
    x - the value of chi-squared
    
    Returns:
    The incomplete gamma function P(a, x).
  - gammq
```
public static double gammq(double a,
           double x)
```
    Returns the incomplete gamma function Q(a, x)= 1 - P(a, x).
    
    Q(a,x) � 1 - P(a,x) � G(a,x)
    G(a)
    �
    �
    �
    x
    e^{- t} t^{a - 1} dt
    
    This is the probability that the observed chi-square will exceed the value of chi-square by chance even for a correct model.
    
    Parameters:
    a - the number of degrees of freedom
    x - the value of chi-squared
    
    Returns:
    The incomplete gamma function Q(a, x)= 1 - P(a, x).
  - gser
```
public static double gser(double a,
          double x)
```
    Returns the incomplete gamma function P(a, x) evaluated by its series representation.
    
    g(a,x) = e^{- x} x^a �
    �
    n = 0
    G(a)
    G(a + 1 + n)
    xⁿ
    
    Parameters:
    a - the number of degrees of freedom/2
    x - the value of chi-squared/2
    
    Returns:
    The incomplete gamma P(a, x) evaluated by its series representation.
  - gcf
```
public static double gcf(double a,
         double x)
```
    Returns the incomplete gamma function Q(a, x) evaluated by its continued fraction representation.
    
    G(a,x) = e^{- x} x^a �
    � 1
    x +
    1 - a
    1 +
    1
    x +
    2 - a
    1 +
    2
    x +
    � �
    � (x > 0)
    
    Parameters:
    a - the number of degrees of freedom/2
    x - the value of chi-squared/2
    
    Returns:
    The incomplete gamma Q(a, x) evaluated by its continued fraction representation.
  - gammln
```
public static double gammln(double x)
```
    Returns the logarithm of the Gamma function of x, for x>0.
    
    G(z) = �
    �
    �
    0
    t^{z - 1} e^{- t} dt
    
    Parameters:
    x -
    
    Returns:
    The value ln(Gamma(x))

Class ChisqProb

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

ChisqProb

Method Detail

gammp

gammq

gser

gcf

gammln