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gammainc

Evaluates the incomplete gamma function.

Prototype

	function gammainc (
		x  : numeric,  
		a  : numeric   
	)

	return_val [dimsizes(x)] :  float or double

Arguments

x

An array of any dimensionality containing the upper limit of integration. x must be (0,1) inclusive, and can only be of type float or double.

a

The shape parameter of the incomplete gamma. It must be the same dimensionality as x.

Return value

The value returned will be the same type and dimensionality as x.

Description

gammainc calculates the cumulative incomplete gamma function. It is often used to determine probabilities. Specifically:

The integral from 0 to X of (1/GAM(A))*EXP(-T)*T**(A-1) DT
where GAM(A) is the complete gamma function of A:
GAM(A) = integral from 0 to infinity of EXP(-T)*T**(A-1) DT

The code used (subroutine cumgam) is from DCDFLIB (Double precision Cumulative Distribution Function LIBrary). This returns the same answers as the Numerical Recipes [Cambridge Univ. Press, 1986] function gammp.

See Also

cdfgam_p, cdfgam_x

Examples

Example 1

 
  a = 10. 
  x = 10. 

  alpha = gammainc(x,a) 
  print("gammainc(x,a)="+alpha)

Output:

  gammainc(x,a)= 0.54207

Example 2

Assume a calculation has been made where the degrees-of-freedom (df=20) and a chi-square value (chi2) has been determined. A significance level may be determined via:

  prob = gammainc( 0.5*chi2, df*0.5 ) 

Example 3

Assume two one-dimensional arrays (bin1, bin2) contain binned data. Further assume bin1 is based upon observations while bin2 is based upon theory:

  df   = dimsizes(bin1) - 1               ; degrees of freedom
  chi2 = sum( (bin1-bin2)^2/bin2 )        ; chi-square statistic

  prob = 1. - gammainc( 0.5*chi2, df*0.5) ; technically, the complementary
                                          ; gamma function